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 46872: Write first four terms of the sequence definded by the recursive sequence
a1 = 4 and an = 3an-1 – 5 for n ≥ 2.
Click here to see answer by fractalier(2101)

Question 46993: What is the degree of the polynomial -4x(to the third power)+2x(to the second power)y-5xy(to the fourth power)
and also
which of the following is a monomial with a degree of 7
a.-2x(to the third power)y( to the second power)
b.4x(to the fourth power)+ 5xy( to the second power)
c.7x
d.x( to the fifth power) yz
Click here to see answer by mathchemprofessor(65)

Question 47001: Write the first four terms of the sequence defined by a[n] = 2n + 3.
Click here to see answer by atif.muhammad(135)

Question 46999: What is the common ration in the geometric sequence 4, -12, 36, -108, . . .?
Click here to see answer by atif.muhammad(135)

Question 47000: Write the first four terms of the arithmetic sequence with a[1] = -6 and d = 4.
Click here to see answer by atif.muhammad(135)

Question 46984: The sequence is defined recursively. Write the first four terms.

I really need some help with this problem please.
Click here to see answer by venugopalramana(3286)

Question 47551: Can u show me how to find the sum of all the complex zeroes of f(x)=x^3-x^2-x+33

Also can u show me how to find a polynominal function of degree 5 with rational coefficient has negative 5,2 minus square root 3, and negative 5 minus 2i
Click here to see answer by stanbon(57361)

Question 47828: Can somebody show me how to solve this.
Evaluate the factorial expression
100!/98! 2!
Thanks!
Click here to see answer by venugopalramana(3286)

Question 47852: I solved this problem but I need somebody to please confirm my answer is right. Thanks.
7
__
\
\ (-1/3)^n = - 547/2187
/
/__
n=0
Sn = ( -1/3)^0 + (-1/3)^1+(-1/3)^2+ (-1/3)^3 +(-1/3)^4+ (-1/3)^5 + (-1/3)^6 +
(-1/3)^7
= 0 + (-1/3) + 1/9 + (-1/27) + 1/81 + (-1/243) + 1/729 + (-1/2187)
= -547/2187
Click here to see answer by Earlsdon(6287)

Question 47859: Please explain how to write the ff. rational number as the quotient of two integers in simplest form.
_
a.0.372
__
b.0.63
Click here to see answer by stanbon(57361)

Question 47826: Can somebody help me with this. Thanks.
Evaluate the series.
7
__ * the broken lines is supposedly a sigma sign.
\
\ 1/k!
/
/__
k= 0
Click here to see answer by Nate(3500)

Question 48068: 8,4,4,4,1/2,1/4,1/8.....
Can you guest what the next term is(the 8th term)? Now can you make a formula which will tell you what the 100th term is?
I guess the next term is 1/16, but I don't know formula to figure out the 100th term.
Click here to see answer by Nate(3500)

Question 48115: Please show me how to do this:
Use the Binomial Theorem to simplify the powers of the complex number:
( 3 + 2i)^3
Click here to see answer by stanbon(57361)

Question 48216: This is not an exact number in my book it is on a worksheet , “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.? Please show how you got your answer
Click here to see answer by stanbon(57361)

Question 48303: I'm not too sure how to write this, but the problem is ... a four is over the sign for sigma and under it is m=1 then (2/m - 2/m+1) I am to write this sum without using sigma notation; then compute the sum. Please help if you can. Thank you!
Click here to see answer by Nate(3500)

Question 48342: i'm not sure if this question is in the right section. its not from a textbook, it is from an algebra II honors summer packet.
it says:
name the sets of numbers to which each number belongs.
use N, W, Z, Q, I, or R.
and the numbers are:
-1/3, sqrt5, and pi.

to me it is very vague, but that is all the information i was given. maybe the letters have a specific meaning that i was never taught. any help at all would be greatly appreciated.
Click here to see answer by stanbon(57361)

Question 48390: Will you please correct my work? Thanks.
Consider a lottery that sells 1000 tickets and awards two prizes. If you purchase 10 tickets, what is the probability that you will win a prize?
My solution: E = 1000
/ \
prizes 2 998 -unlucky numbers
1 1
E= 2C1 x 998C1 = 1996
S= 1000C2 = 499500
P= 1996/499500= .003996

Click here to see answer by cowess(34)

Question 48705: Find the nth term of a sequence whose first several terms are given.
1, 1/2, 3, 1/4, 5, 1/6...
I know every other number has 2 added to it but I can't get the formula for the fractional component sequence members,
Thank you so very much!
Click here to see answer by stanbon(57361)

Question 48671: what would be the expression for the pattern 1, 3, 9, 27 (not just timesing by three but using an algebra expression where n= 1,2,3,4 etc... and the answer is 1, 3, 9, 27
Click here to see answer by stanbon(57361)

Question 48756: Use the arithmetic sequence of numbers 2, 4, 6, 8, 10, what is the sum of the first 30 terms? I came up with 930, am I correct?
Also how do I type in the term or subscript? Ex: a1 a2 a3.....
Click here to see answer by AnlytcPhil(1277)

Question 48744: Write the sum without using sigma notation:
n over (capital sigma)j=1(under) (-1)^j+1 x^j
Thank you very much!
Click here to see answer by kev82(148)

Question 49213: Represent each repeating decimal as the quotient of two intergers.
_
0.5 =0.5555
Thank you, Michelle
Click here to see answer by AnlytcPhil(1277)

Question 49213: Represent each repeating decimal as the quotient of two intergers.
_
0.5 =0.5555
Thank you, Michelle
Click here to see answer by atif.muhammad(135)

Question 49212: Expand Problems using the binomial formula
(2x-y)^6
Thank you, Michelle
Click here to see answer by AnlytcPhil(1277)

Question 49877: For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
P(x) = x4 + 3x3 - 4x2 + 6x - 38; 2
Click here to see answer by venugopalramana(3286)

Question 50261: i've tried to figure this out for fifteen minutes and can't. Will you please help me?
[(31a-36b)-21c]-[19a-(39c+43b)]
Click here to see answer by hulamc723(15)

Question 50261: i've tried to figure this out for fifteen minutes and can't. Will you please help me?
[(31a-36b)-21c]-[19a-(39c+43b)]
Click here to see answer by stanbon(57361)

Question 50375: Find the sume of this series.
28+35+42+49+......728.
I know this is 7 added each time. But stuck on the equation to figure.

Click here to see answer by stanbon(57361)

Question 50531: 0, 1, 8, 27, 64
i need to suppy the next 3 terms for the sequence and describe how i found the next 3 numbers. ive tried to multiply it but the have no common numbers and ive tried adding but they dont match up! it would help me a lot! thank you for your help!
Click here to see answer by Nate(3500)

Question 51048: -(-2)3
Click here to see answer by checkley71(8403)

Question 51322: Between 2 numbers whose sum is 13/6,an even number of arithmetic mean's are inserted,the sum of these numbers exceeds their number by unity,how many means are there?
Click here to see answer by venugopalramana(3286)

Question 51319: The number of terms in a Arithmetic progression is even,the sum of the odd terms is 24 and sum of the even terms is 30 and if the last term exceeds the first term by 21/2,find the numbers
Click here to see answer by venugopalramana(3286)

Question 51387: 69.72=68.9257x + 70.9249(1-x)
Click here to see answer by rchill(405)

Question 51321: The value of xyz is 15/2 or 18/5 accordingly if the series a,x,y,z,b is arithmetic progression or harmonic progression.Find a,b.
Click here to see answer by venugopalramana(3286)

Question 51695: If x>0,y>0,z>0 and x+y+z=1,prove that
Click here to see answer by darq(90)

Question 52292: a ramp in a multistory car park is 62 feet long and rises 11 feet. estimate the angle that the ramp makes with the horizontal.
please help me figure this out.
i dont know how.
thanks a lot!
Click here to see answer by funmath(2925)

Question 52441: An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
a) Find the function V that represents the volume of the box in terms of x.
Answer

b) Graph this function and show the graph over the valid range of the variable x..
Show Graph here

c) Using the graph, what is the value of x that will produce the maximum volume?
Answer

Click here to see answer by venugopalramana(3286)

Question 52439: 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:
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.)? Express your observations as a general formula in "n."
Answer:

Click here to see answer by venugopalramana(3286)

Question 52438: Use the geometric sequence of numbers 1, 2, 4, 8,…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 24th 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 52436: 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?
Answer:
Show work in this space.

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.
Answer:
Show work in this space.

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.
Answer:
Show work in this space.

d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
Click here to see answer by AnlytcPhil(1277)

Question 52444: Is it possible to find a sequence with the rule add 7 for which
all the terms are multiples of 7
all terms are multiples of 5
all terms are even numbers
every 7th terms is a prime number
Please could I have an example
Click here to see answer by stanbon(57361)

Question 52539: 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

Click here to see answer by checkley71(8403)

Question 52642: 4) John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.
Show clearly the algebraic steps which prove your dimensions are the maximum area which can be obtained. Use the vertex form to find the maximum area.
Answer:
Show work in this space.

Click here to see answer by checkley71(8403)

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