How do you find the sum of the geometric series 1/16+1/4+1+... to 7 terms?

2 Answers
Nov 12, 2016

4^(-2)(1-4^7)/(1-4)=5461/16

Explanation:

By collecting 4^(-2) the progression can be rewritten as

4^(-2)(1+4+4^2+....+4^6)
in general we know that 1+q+q^2+....+q^n=(1-q^(n+1))/(1-q)
in our case we have 4^(-2)(1-4^7)/(1-4)=5461/16

Nov 13, 2016

The sum of the first 7 terms is 5461/16= 341 5/16

Explanation:

The formula for the sum of a particular number of terms of a geometric sequence is

S_n=frac{a_1(1-r^n)}{1-r} where

a_1=the first term of the sequence

r= the common ratio

To find r, divide a term by the previous term.

To find the sum of the first 7 terms of the sequence 1/16, 1/4, 1...

a_1=1/16

r=1/4 -: 1/16=4

n=7

S_n= frac{1/16(1-4^7)}{1-4} = 5461/16=341 5/16