What is S7 for 2+4+8+16+......? Please show steps for how you got the answer

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Answer 1 · 2018-06-03T03:27:52

$S_7 = 254$

This series sum is: $S_n = sum_(i=1)^n 2^i$

The series is a Geometric Progression (GP) with first term $a_1 = 2$ and common ratio $r=2$

The sum of the first $n$ terms of a GP is given by:

$S_n = (a_1(1-r^n))/(1-r)$

Therefore, in this case,

$S_7 = (2(1-2^7))/(1-2)$

$= (2(1-128))/-1$

$=254$