Question

Look at the following sequence.

54, 36, 24, 16, . . .


If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose “not geometric.”

Answer 1

`r \: = \: \boxed{ \bold{(2)/(3) }}`

Explanation:

• Calculate the ratio of the progression by dividing a term of it by the immediately preceding one.

`r \: = \: (36)/(54) \\ \\ r \: = \: (24)/(36) \\ \\ r \: = \: (16)/(24)`

• We simplify the fractions:

`r \: = \: (2)/(3) \\ \\ r \: = \: (2)/(3) \\ \\ r \: = \: (2)/(3)`

Since the ratio is the same, that is the common ratio.

MissSpanish