Question

What is the sum of the first ten terms of the sequence 4, -12, 36, -108 . . . ?

Answer 1

Given :   4  , -12 , 36 , - 108

To Find :  sum of the first ten terms of the sequence

Solution:

4  , -12 , 36 , - 108

-12/4 = -3

36/(-12) = -3

-108/36 = -3

Hence common ratio = - 3

This is an geometric sequence

a = 4

r = -3

Sₙ =  a(rⁿ - 1)/(r - 1)

n = 10

S₁₀ = 4 ( (-3)¹⁰ - 1) /(-3 - 1)

= 4( 59049 - 1)/(-4)

= -(59048)

sum of the first ten terms of the sequence = -59048

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