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.
