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

Vrbljanovwu

Vrbljanovwu

Answered question

2022-09-30

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

Answer & Explanation

Corbin Hanson

Corbin Hanson

Beginner2022-10-01Added 10 answers

the sum to n terms of a geometric sequence is
x S n = a ( r n - 1 ) r - 1
where a is the first term and r the common ratio
here a=4 and r=−2
S 5 = 4 ( ( - 2 ) 5 - 1 ) - 2 - 1
S 5 = 4 ( - 32 - 1 ) - 3 = - 132 - 3 = 44
Alternatively
listing the first five terms of the sequence
4,−8,16,−32,64
S 5 = 4 - 8 + 16 - 32 + 64 = 44

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