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 39310: Need help solving assingment due tongiht.
1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:
a) What is d, the difference between any 2 terms?
Answer:
Show work in this space.

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.)?
Answer:
Click here to see answer by venugopalramana(3286)

Question 39308: Need help solving assignment due tongiht.
2) 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.

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 venugopalramana(3286)

Question 39436: Evaluate the series if it converges.
9 + 27/4 + 81/16 + 243/64
Click here to see answer by AnlytcPhil(1276)

Question 39436: Evaluate the series if it converges.
9 + 27/4 + 81/16 + 243/64
Click here to see answer by astromathman(21)

Question 39435: Find a1 of arithmetic sequence from given information.
a7=-45 a15=-77
Click here to see answer by AnlytcPhil(1276)

Question 39453: Please help. I do not understand at all. Thanks for all the help.
Details: Using the index of a series as the domain and the value of the series as the range, is a series a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally
Click here to see answer by Nate(3500)

Question 39485: Using the index of a series as the domain and the value of the series as the range, is a series a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.
Click here to see answer by stanbon(57250)

Question 39455: Please help.
2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Show work in this space.

b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: the sum of the first 10 terms is: 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 stanbon(57250)

Question 39454: Please help.
2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Show work in this space.

b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: the sum of the first 10 terms is: 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 venugopalramana(3286)

Question 39508: I really need some help!! (Fast!!!!) Please....
Using the index of a series as the domain an dthe value of the series as the range, is the series a function?
Include in ans:
Which one of the basic functions(linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real life examples of both arithmetic and geometric sequences and series. Explain how these might affect you personally?

2. Use the arithmetic sequence of numbers 2,4,6,8,10...to find the following:
a) What is d, the difference between any 2 terms?
Ans:
Show work below:
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Ans:
c) Using the formula for the sum of an aritmetic series, what is the sum of the first 20 terms?
Ans:
d) Using the formula for the sum of an aritmetic series, what is the sum of the first 30 terms?
Ans:
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..)?
Click here to see answer by venugopalramana(3286)

Question 39188: I am not sure if this question is in the proper place, but somebody please help. I do not understand.
Using the index of a series as the domain and the value of the series as the range, is a series a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.
Click here to see answer by venugopalramana(3286)

Question 39510: write out the term of the geometric sequence that satisfies the given conditions.
a1=-9,r=-9/10,n=5
Click here to see answer by fractalier(2101)

Question 39509: Find the sum of the first n terms of the given arithmetic series.
a2=-6, a5=-18 (n=8)
Click here to see answer by venugopalramana(3286)

Question 39509: Find the sum of the first n terms of the given arithmetic series.
a2=-6, a5=-18 (n=8)
Click here to see answer by Fermat(127)

Question 39635: 4) 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 Crane came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Crane 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 on the third square. Continue this until all 64 squares are covered with grains of wheat.” As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved.
a)How much wheat would Mr. Brown have to put on the 24nd square?
Show work in this space.

b)How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
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 provide the answer in either scientific notation, or calculate and show all 20 digits.
Answer:
Click here to see answer by venugopalramana(3286)

Question 39633: I'm not sure this is the right forum to ask but I would like to find out what number comes next in this sequence? 3692, 738, 584, 232, ???
Thanks for your help!
enjel
Click here to see answer by atif.muhammad(135)

Question 40061: Use the indicated property to write an expression that is equivalent to the following expression.
(7 + 11) + 2 (associative property of addition)
Click here to see answer by fractalier(2101)

Question 40302: Hello!
Here's a tutor who is a bit rusty on this subject. Is there a simple expression for the following sum?

For example,
1 + 4 + 9 + 16 + ... + 100
or
25 + 36 + 49
etc.
Thank you very much!
Click here to see answer by venugopalramana(3286)

Question 40523: factor completely
3x2+16x+20
Click here to see answer by josmiceli(9661)

Question 40853: a1= 2
r= 3
Formula is Sn =
Here n =6, so S6 = = 728
Click here to see answer by psbhowmick(529)

Question 40979: solve the arithmetic sequence
a5=-2 and a13=30
Click here to see answer by psbhowmick(529)

Question 40980: find the sum of the first n terms of the given arithmetic series
a1=-13,a7=20.8 (n=7)
Click here to see answer by stanbon(57250)

Question 41117: Find the sum of the geometric Series: 4,-2,-1/2,.....Answer should be a fraction.
Click here to see answer by stanbon(57250)

Question 41115: Find the third term in the expansion of:(e-2f)^8
Click here to see answer by stanbon(57250)

Question 41611: Use the Binomial Theorem to find the third term in the expression of (n-2p)^6.
Thanks
Click here to see answer by venugopalramana(3286)

Question 41742: what are the next two numbers in this sequence and what is the difference between the terms:
3, 7, 14, 23, 36, _, _
Click here to see answer by abcdefg(37)

Question 41799: Use the binomial theorum to find the fifth term in the expansion (2x+3y)^5.
Thank You
Click here to see answer by fractalier(2101)

Question 41798: Find the first three iterates x(1), x(2), x(3) of f(x) = 2x-5 for an initial value of x(0) = 3.
Thank You
Click here to see answer by fractalier(2101)

Question 41795: Find the sum of the infinite geometric series 36 + 24 + 16 +... if it exists
Click here to see answer by fractalier(2101)

Question 41801: Find a counter-example to the statement 4^n+1 is divisible by 5.
Thank You
Click here to see answer by fractalier(2101)

Question 41796: Find the first five terms of the sequence for which a(1)=5 and a(n+1)= 3a(n)+1.
Thank You
Click here to see answer by fractalier(2101)

Question 41806: Students are given a list of ten vocabulary words to learn. In how many ways could four of the words be listed on a test?
Click here to see answer by fractalier(2101)

Question 41805: A scout troop will prepare trail mix for their next hike. They have decided to mix one type of nut, one type of dried fruit, and one type of granola. The local store carries 8 types of nuts, 6 types of dried fruit, and 5 types of granola. How many different trail mixes are possible?
Thanks
Click here to see answer by fractalier(2101)

Question 41935: Find the sum of a geometric series for which a(1)=1, r=2, and n=6
Thanks you
Click here to see answer by fractalier(2101)

Question 41934: Find four geometric means between 4096 and 972.
Thank you
Click here to see answer by fractalier(2101)

Question 41934: Find four geometric means between 4096 and 972.
Thank you
Click here to see answer by AnlytcPhil(1276)

Question 41933: Find the next two terms of the geometric sequence 6250,5000,4000,...
Click here to see answer by fractalier(2101)

Question 41936: Find a(1) in a geometric series for which S(n) =189, r=1/2, and a(n)=3.
Thank you
Click here to see answer by venugopalramana(3286)

Question 41931: Find the three arithmetic means between 21 and 13.
Click here to see answer by fractalier(2101)

Question 41932: Find S(n) for the arithmetic series in which a(1)=-11, a(n)=13, and n=7.
Thank you
Click here to see answer by venugopalramana(3286)

Question 41932: Find S(n) for the arithmetic series in which a(1)=-11, a(n)=13, and n=7.
Thank you
Click here to see answer by fractalier(2101)

Question 41804: Find a(1) in a geometric series for which S(n) = 189, r = 1/2, and a(n) =3.
Thanks
Click here to see answer by venugopalramana(3286)

Question 42050: Please sir , send me the value or method to find the value of the following summation.

sum of ( a^n * b^n ) / (n ! )2

here a and b are non negative real constants and summation is over n where n varies 0 to infinity.
Click here to see answer by psbhowmick(529)

Question 42186: 256, 64, 16, 4..
is this sequence geometric, arithmetic, or neither
Click here to see answer by psbhowmick(529)

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