SOLUTION: What is the fifth term of a geometric sequence whose first term is 32,768 and common ratio is one fourth?

Question 1108567: What is the fifth term of a geometric sequence whose first term is 32,768 and common ratio is one fourth?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the first term is 32768 and the common ratio is 1/4, then each succeeding term in the sequence is 1/4 * the value of the preceding term.

if you let the first term be x, then the second term is 1/4 * x and the 3d term is 1/4 * that and the 4th term is 1/4 * that and the 5th term is 1/4 * that.

you get x * 1/4 * 1/4 * 1/4 * 1/4 which is equal to x * (1/4) ^ 4.

so the first term in the geometric sequence is 32768 * (1/4) ^ 4.

that makes it equal top 128.

the general formula says An = A1 * r ^ (n-1)

A1 = 32768
r = 1/4
n = 5

using this formula, you get A5 = 32768 * (1/4) ^ 4.

if you work by multiplying each succeeding term by 1/4, you get:

A1 = 32768
A2 = A1 * 1/4 = 8192
A3 = A2 * 1/4 = 2048
A4 = A3 * 1/4 = 512
A5 = A4 * 1/4 = 128

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