SOLUTION: Find S8 for the geometric series 256 + 64 + 16 + 4 +�

Question 398922: Find S8 for the geometric series 256 + 64 + 16 + 4 +�
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this is a geometric series with a common ratio of 1/4.

formula for sum of a geometric series is:
Sn = (a*(1-r^n)) / (1-r)
n = number of terms in the series.
S = sum of the terms in the series.
a = the first term in the series.
r = the common ratio in the series.

In this problem:

n = 8
a = 256
r = (.25)

Substitute in the formula to get:

Sn = (a(1-r^n)) / (1-r) becomes:

S8 = (256 * (1 - .25^8)) / (1 - .25)

Simplify to get:

S8 = (256 * (1 - .000015259) / (.75)

Simplify further to get:

S8 = (256 * .999984741) / (.75)

Solve to get:

S8 = 341.328125

You can verify this is correct by detailing each individual term from 1 to 8 and then summing them up.

You get:
S1 = 256
S2 = 64
S3 = 16
S4 = 4
S5 = 1
S6 = .25
S7 = .0625
S8 = .015625

Sum is equal to 341.328125

Answer is the same.

You're good.

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