Find the common ratio of the sequence -172 -86 -43 -21.5

Solution:

Given sequence is -172 -86 -43 -21.5,...

Common ratio = t₂ / t₁ = -86 / -172 = 1 / 2 

Also t₃ / t₂ = -43 / -86 = 1 / 2 

The ratio 1/ 2 is the same in the sequence, hence called the common ratio.

In general if a₁, a₂, a₃, a₄,..., a_n are n terms of geometric progression then,

Common ratio, r = a_n /a_{n - 1} where a_n is the n^th term of the geometric progression and a_{n - 1} is the (n - 1)^th term of the geometric progression

Find the common ratio of the sequence -172 -86 -43 -21.5

Summary:

The common ratio of the sequence -172 -86 -43 -21.5 is 1/2.