Question

What is the sum of the first 7 terms of the geometric series below? 1,2,4,8, ,,

Answer 1

S₇ = 127

Explanation:

the sum to n terms of a geometric series is

`S_(n)` =
`(a_(1)(r^n-1) )/(r-1)`

where a₁ is the first term and r the common ratio

here a₁ = 1 and r =
`(a_(2) )/(a_(1) )` =
`(2)/(1)` = 2 , then

S₇ =
`(1(2^7-1))/(2-1)` =
`(2^7-1)/(1)` =
`2^(7)` - 1 = 128 - 1 = 127

Answer 2

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