Question 398922
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.