The first term of a geometric sequence is 4 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?

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Answer 1 · 2016-01-25T17:44:32

first term $=a_1=4$ , common ratio $=r=-2$ and number of terms $=n=5$

Sum of geometric series up to $n$ tems is given by

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

Where $S_n$ is the sum to $n$ terms, $n$ is number of terms, $a_1$ is the first term, $r$ is the common ratio.

Here $a_1=4$ , $n=5$ and $r=-2$

$implies S_5=(4(1-(-2)^5))/(1-(-2))=(4(1-(-32)))/(1+2)=(4(1+32))/3=(4(33))/3=4*11=44$

Hence, the sum is $44$