Question

Classify each sequence as arithmetic, geometric or neither -1/16,1/4,-1,4,-16

Answer 1

geometric sequence

Explanation:

A geometric sequence has a common ratio r between consecutive terms

`(a_(2) )/(a_(1) )` =
`((1)/(4) )/(-(1)/(16) )` =
`(1)/(4)` × - 16 = - 4

`(a_(3) )/(a_(2) )` =
`(-1)/((1)/(4) )` = - 4

`(a_(4) )/(a_(3) )` =
`(4)/(-1)` = - 4

`(a_(5) )/(a_(4) )` =
`(-16)/(4)` = - 4

there is a common ratio r = - 4 between consecutive terms.

Then the sequence is geometric