Question

For the following exercises, determine whether the sequence is geometric. If so, find the common ratio. 

−6, −12, −24, −48, −96, ...

Answer 1

Consider the following sequence,

{-6, -12, -24, -48, -96, … } ...... (1)

 

Find whether the above sequence is geometric or not, divide each term by its previous term,

a2 ÷ a1 = (-12) ÷ (-6)

              = 2

Divide third term by second term,

a3 ÷ a2 = (-24) ÷ (-12)

             = 2

 

Divide fourth term by third term,

a4 ÷ a3 = (-48) ÷ (-24)

             = 2

 

Divide fifth term by fourth term,

a5 ÷ a4 = (-96) ÷ (-48)

             = 2

 

As the ratio of any two consecutive terms is constant, the above sequence is “Geometric.”

 

The common ratio between any two consecutive terms is equal to 2, the common ratio of the geometric sequence will be r = 2.

The common ratio between any two consecutive terms is equal to 2, the common ratio of the geometric sequence will be r = 2.