How do you find the sum of the first 5 terms of the geometric series: 4+ 16 + 64…?

1 Answer
SagarStudy
Dec 29, 2015

1364

Explanation:

a_2/a_1=16/4=4
a_3/a_2=64/16=4

implies common ratio=r=4 and a_1=4

Sum of a geometric series is given by
Sum=S=(a(1-r^n))/(1-r)

Where a is the first term r is the common ratio and n is the number of terms.

Sum=S=(4(1-4^5))/(1-4)=(4(1-1024))/(-3)=(4(-1023))/(-3)=(-4092)/(-3)=1364

Hence the required sum is 1364.

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