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

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

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