Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

Tutors Answer Your Questions about Sequences-and-series (FREE)

Question 59091: Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.
You can this r easily by taking the ratios

b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer:
Show work in this space.

c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer:
Show work in this space.

Click here to see answer by jayanthi(5)

Question 59396: CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains of wheat on the third square. Continue this until all 64 squares are covered with grains of wheat.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of whaet involved.
a) How much wheat would Mr. Brown have to put on the 24nd square?
Answer:
Show work in this space

b) How much total grain would the traveling salesman receive in total if the checkerboard only had 24 squares?
Answer:
Show work in this space

c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? please answer in either scientific notation, or calculate and show all 20 digits
Answer:
Show work in this space

Click here to see answer by Edwin McCravy(8880)

Question 60451: hi, I'm Sarah and i'm in 10th grade taking algebra 2, but i'm also taking an SAT prep course, and i'm having a little trouble with questions involving finding the nth term. it's quite a bit more advanced than regular math, but i hope you can still give me a hand. here is an example of one of the problems i was given:
Instructions: writs the general term of the sequence:
1,8,27,64,125,...
(answer goes here) -> Nth term:
i was also given problems using variables; but i can't understand them without first understanding how to find the answer using numerical values. i would be most appreciative if you could also work one of the questions with variables so i can get an idea of how to work them. here is a question with variables:
The sequence a, a+d, a+2d, a+3d, a+4d,... has as it's Nth or general term (answer goes in blank) -> _________
thank you in advance for your help!
Click here to see answer by hayek(51)

Question 60460: mama mia! for some reason, these sequences are just driving me mad! i would appreciate if you could help me with a few more problems. hopefully, something will click in my head after this.
Instructions: write the general term of the sequence:
#1. 1,2,3,4,5,6,...
(answer here) -> Nth term:____
i'm pretty sure the answer is just plain N, but i'm not sure.
#2. 1,2,4,8,16,...
(answer here) -> Nth term: ___
I know the answer involves the number 2 and N, but i'm not sure how to put them together correctly.
#10. 1,-1,1,-1,1,-1,...
Nth term:__
this one just left me clueless. i think it's -1n^0, but, i'm not sure.
#9. -1,4,-9,16,-25,...
Nth term:__
again, i think it's -n^3, but i'm not positive.
I'm also having trouble with adding terms in a sequence. i have a formula: [(first term + last term)(number of terms)]/2. but i'm not sure how i would apply it to sequences involving exponents.
Instructions: write the sum
#2. 1+3+9+27+81+...+1*3^101
Now, am i correct in assuming that 1*3 is the general term of the sequence and that the last term is the 101st value of 1*3?
#5 2+7+12+17+...+97
just plain lost on this one.
again, i thank you for your help in advance

Click here to see answer by josmiceli(9649)

Question 60971: To whom may it concern,
I have difficulty to answer this question.
To find the width of a river, a boy places a wooden peg at a point A on one side directly opposite an object B on the opposite bank. From A, he walks 50 m along the bank to a point C. He observes that ACB = 34°. Calculate the width of the river.
Please help. Thanks in advanced.
CH Lam
Click here to see answer by ankor@dixie-net.com(15624)

Question 61045: The instructions are to tell whether each series has a sum. if it does give its value.
The problem is 0.7 + 0.07 + 0.007 + 0.0007
i have no clue how to solve this
Please help
Click here to see answer by joyofmath(189)

Question 61044: Hey,
I have a problem where the instructions say : Tell Whether each series has a sum. If it does, give its value
the problem i need help with is 2/3 + 1 + 3/2 + 9/4...
i dont know how to get the answer or how to find it
Click here to see answer by joyofmath(189)

Question 60972: To whom may it concern,
I have encountered problem to do this question.
The angle of elevation of the top of a post from a point on level ground 38 m away its 33.23°. Find the height of the post.
Please help. Thanks a lot.
CH Lam
Click here to see answer by josmiceli(9649)

Question 61046: i dont understand this one
it is The sigma sign, with the infinity sign on the top of it, K=1 below it, and to the right of it

oh my god please help ! =]
Click here to see answer by oberobic(2304)

Question 60973: To whom may it concern,
I have trouble to do this question.
The length and width of a triangle are 19.2 cm and 12.4 cm respectively. Find the angle between a diagonal and the shorter side of the triangle.
Please help. Thank you very much.
CH Lam
Click here to see answer by uma(370)

Question 60970: To whom may it concern,
I have trouble to get the answer for the follwoinh questions.
A bank charges 2.25% per month simple interest on personal loan. If John borrows $6400 for a period of 2 years and 1 month, find the total interest he has to pay.
Please help. Thank you very much.
CH Lam
Click here to see answer by uma(370)

Question 61575: 4.(3+2)=(3+2).4 Identify the property that is used.
Click here to see answer by asha(30)

Question 62129: Find three consecutive numbers whose sum is 126? Could you show the steps for me.
Click here to see answer by joyofmath(189)

Question 62129: Find three consecutive numbers whose sum is 126? Could you show the steps for me.
Click here to see answer by stanbon(57222)

Question 62204: what is the three consecutive numbers whose sum is 126?
Click here to see answer by 303795(595)

Question 62317: Solving systems by elimination
how do i solve this:
{2 over 3x -3y = 1 over 5
{2x-9y =4
i know you have to find out what x and y equiels to but i don't know how.
Click here to see answer by ankor@dixie-net.com(15624)

Question 63055: Find all the real zeros of function f(x)=12x^4+35x^3+144x^2+114x+20
I already have x= -2/3
Click here to see answer by stanbon(57222)

Question 63000: Please help me with the following :
Find three consecutive even integers such that 6 times the first is 16 less than four times the sum of the second and third.
thank u
Click here to see answer by 303795(595)

Question 63271: I am having trouble on this homework problem. Any help would be appreciated. Thank you.
If a6=-17 and S6=-12 find a1 and d
Click here to see answer by uma(370)

Question 63423: 1. prove that:
n²-1000n-> infinity as n-> infinity
2. use standard results to show that:
n^2-3n+1/n+5 ->infinity as n->infinity

Click here to see answer by Edwin McCravy(8880)

Question 63561: I need help on this homework problem. Thank you for any help you can provide.
a1=1 r=-1 find s20
I keep getting 1 as the answer but the answer is 0. what am I missing?
Click here to see answer by stanbon(57222)

Question 63316: find the first four terms of the sequence a) a[n]=n^3+1
b) a[1]=4;a[n]=3a[n-1]+1
thank you...
Click here to see answer by venugopalramana(3286)

Question 64423: Use the geometric sequence of numbers 1, 2, 4, 8,... to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the nth term of a geometric sequence, what is the 24th term?
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Click here to see answer by Edwin McCravy(8880)

Question 64422: Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,...to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.
d) What observation can you make about these sums? In particular, what whole number does it appear that the sum will always be smaller than?
Click here to see answer by Edwin McCravy(8880)

Question 64676: I am having problems with this. I think I have figured out the first one. Thanks in advance for any help.
Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any 2 terms?
Answer: d = 2
Show work in this space.
1 +2 =3 + 2 =5 + 2 = 7 etc.

b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.

c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Show work in this space

d) Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Show work in this space

e) What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n."
Answer:

Click here to see answer by stanbon(57222)

Question 65064: I am so lost on this. Please help....
CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space

b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
Show work in this space

c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?
Answer:
Show work in this space

Click here to see answer by stanbon(57222)

Question 65199: Find the sum of the geometric series: 1 + 1/4 + 1/16 + 1/64...
I tried to do the series but the formula in the turorial was ocnfusing to me. Thanks for any help!
Click here to see answer by joyofmath(189)

Question 65369: Can someone tell me how to input a factorial (!) equation to find the first 5 terms into a TI-83?
For example: b{n}=((n+2)!)/n!
Thank you.
Click here to see answer by stanbon(57222)

Question 65388: Find the Arihmetic means of the sequence
23, ___, ____, ____, 67
Click here to see answer by stanbon(57222)

Question 65389: Find the first three terms of the arithmetic series in which asub1= 5 asubn= 33 and Ssubn= 152
Click here to see answer by stanbon(57222)

Question 65391: Find the common ratio of the geometric sequence
81, -27, 9, -3, ...
Click here to see answer by stanbon(57222)

Question 65393: find asub 1 for each geometric series described
1. Ssubn= 45/8 r=1/2 n=4
2. Subn=-242 r=3 n=5
Click here to see answer by stanbon(57222)

Question 65390: Find the geometric means of each sequence
1. 9,___, ____, -243
2. 1.5, ___, ___, ___ 384
Click here to see answer by stanbon(57222)

Question 65514: Hello.
I have no idea how to solve the following problem. Apparently, our teacher forgot to go over it. I just need help on where to start. Perhaps you can give me an example?
The problem is as follows:
Simplify:
(n+3)! / (n+1)!
Thank you for your help.
Click here to see answer by stanbon(57222)

Question 65392: Find the sum of each geometric series described
1. asub1= 512 r=1/2 n=6
2. 3 + 6 + 12...+192
3. asub1= -2 asub5= -162 n=7

Click here to see answer by venugopalramana(3286)

Question 65739: Please help me figure out this word problem. Considering yourself, your parents, your grandparents, and so on, back to your grandparents with the workd "great" used in front 40 times. What is the total number of people that you are considering. Thanks for your help.
Click here to see answer by ntnk(54)

Question 65740: Another problem I need a little help with.
Find the sum of the infinite geometric series if possible.
-1+(1/4)-(1/16)+(1/64)....
I multiplied by 4 and came up with 4s=-4+1-(1/4)+(1/16). What do I do next? Or maybe it's not possible to find the sum.....???
Thanks
Click here to see answer by praseenakos@yahoo.com(507)

Question 64566: Hi. I need help on how to solve the following problem. I've tried solving it many times but couldn't get the correct answer.
Find the partial arithmetic sum of the second set of 100 even terms. (102-200)
Click here to see answer by venugopalramana(3286)

Question 65758: Please help me find the sum of this finite geometric series.
2+10+50+250+1250. So far I have a=2, r=5 and n=126. Using the formula
Ssubn=(a(1-4^n))/1-r, I have Ssub126=(2(1-5^126))/1-5. This is where things get out of hand. On my calculator I come up with 5.877x10^87. This is supposed to add up to 1562.
Click here to see answer by ptaylor(2048)

Question 65876: Regarding question #65739. The one about the number of people when counting yourself through your great grandparents using 40 "greats". Since the number obtained is roughly 1000 times the number of people that have ever lived, this is absurd. There must be something wrong with the reasoning. What is it?
Click here to see answer by Edwin McCravy(8880)

Question 65997: here's the sequence/pattern:
1, -1, 2, -2, 3,....
how would u explain the pattern besides the fact that it goes in order and after the positive number you put the opposite of it?? or is that all?? or is some addition/subtraction involved??
Click here to see answer by Edwin McCravy(8880)

Question 66130: the third and fourth terms of a sequence are 26 and 40. if the second differences are a constant 4, what are the first five terms of the sequence.
Click here to see answer by josmiceli(9649)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645