Question

Consider this sequence: -81, -54, -36, -24, … . The sequence is . The common ratio of the sequence is . The sum of the first five terms of the sequence is

Answer 1

A1 = - 81, a2 = - 54, a3 = - 36, a4 = - 24,...
The sequence is geometric sequence.
r = a2/a1 = (-54)/(-81) = 2/3
The common rate of the sequence is 2/3.
The sum of the first 5 terms:
S 5 = a1* (1-(2/3)^5) / (1-2/3) =
= 81 * ( 1- 32/243)/ (1/3) = 
= 81 * ( 211*81 ) = 211 

Answer 2

We have the following remark
-81/-54= -54/-36 = -36/ -24=...= 1.5
the sequence is geometric sequence
the common ratio of the sequence is 1.5
the sum of the five terms of the sequence is 
S5= a[1- (1.5)^5  / 1-1.5],  a first term, 
S5= -42*6.5= - 276