Question

What is the sum of the geometric sequence −3, 18, −108, … if there are 7 terms? −719,835 −119,973 119,973 719,835

Answer 1

Sn = a1 (1-r^n) / (1-r)
= -3 (1- (-6)^7) / (1-(-6))
= -3 (1-(-279936)) / 7
= -3 (279937) / 7
= -119,973 #

Answer 2

The correct option is: -119,973

Explanation:

Geometric sequence: -3, 18, -108, ..............

First term,
`a_(1)= -3`

Common ratio,
`r= (a_(2))/(a_(1)) =(18)/(-3)= -6`

Number of terms in the sequence,
`n= 7`

Sum of n terms:
`S_(n)= (a_(1)(1- r^n))/(1-r)`

So, sum of 7 terms,

`S_(7)= (-3[1-(-6)^7])/(1-(-6)) = (-3(1+279936))/(1+6)=(-839811)/(7)=-119973`