Using the formula for the nth term of a geometric sequence, what is the 24th term
Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
2006-07-04 07:23:23 · 11 answers · asked by brownsugar20006 1 in Science & Mathematics ➔ Mathematics
The answer to the first part is 2^(n-1), so the twenty-fourth term is 2^23.
By observation, the sum of the first n terms is 2^(n)-1, so the sum of the first 10 terms is 2^10-1. I don't think that always works, but it does in this case.
2006-07-04 07:32:00 · answer #1 · answered by anonymous 7 · 0⤊ 0⤋
The general formula for this is:
Give the series
a + a*(r) +a*(r^2) + a*(r^3) +... a*(r^n)
The n-th term is a*(r^(n-1) )
The sum of n terms is
(a -a*(r^n) )/(1-r)
In your example
The 24th term is 1*(2^23) = 2^23 =8388608
The sum of the 10 terms is
(1 - 1*(2^10) )/(1-2) = (1- 2^10)/(-1)
= 2^10 -1 = 1023
2006-07-04 23:21:59 · answer #2 · answered by PC_Load_Letter 4 · 0⤊ 0⤋
Use the formula, it should be in your book.
1st answer
plug 1 for T1, because its the first term. Plug 2 for r, because that is what you are multiplying each time. for n, put 24
The 24th term is 8388608
2nd answer
plug 1 for T1, plug 2 for r, and plug 10 for N
the sum of the first 10 terms is 1023
2006-07-04 14:36:58 · answer #3 · answered by Hi My Name is 2 · 0⤊ 0⤋
24th term = 2^(24-1)
sum(t(1 TO 10)) = 2^(10) - 1 = 1023
2006-07-04 14:59:37 · answer #4 · answered by Anonymous · 0⤊ 0⤋
the 24 th term is 2^23
then sum of first 24 terms is:
2^10-2
2006-07-04 14:36:26 · answer #5 · answered by codemastercool 2 · 0⤊ 0⤋
5/6
2006-07-09 23:23:32 · answer #6 · answered by Andy J 1 · 0⤊ 0⤋
You really don't want to have someone give you the answer to this question, I'm sure that you already have it and are just playing with us. So now we'll give you a chance to show off and tell us the answer. If it's right you get the prize.
2006-07-04 14:31:02 · answer #7 · answered by olemerv2000 2 · 0⤊ 0⤋
24th term is 2^23 or 8,388,608
Sum of the first ten terms is 1,023.
You will learn more if you try doing the problems yourself.
2006-07-04 14:31:28 · answer #8 · answered by Pascal 7 · 0⤊ 0⤋
an = a1*r^(n - 1)
an = 1 * 2^(n - 1)
an = 2^(n - 1)
2^(24 - 1)
2^(23)
8388608
-----------------------------------
Sn = (a1(1 - r^n))/(1 - r)
Sn = (a1(1 - 2^n))/(1 - r)
S(10) = (1(1 - 2^10))/(1 - 2)
S(10) = (1 - 1024)/(-1)
S(10) = (-1023)/(-1)
S(10) = 1023
2006-07-04 14:33:22 · answer #9 · answered by Sherman81 6 · 0⤊ 0⤋
Great. So you'll get the answer from here, put it in your homework and the teacher will go "Wow... great work! You're the only one who found the answer! Please, explain to us how you did this task!"
...then we'll laugh.
2006-07-04 14:28:14 · answer #10 · answered by Lyvy 4 · 0⤊ 0⤋