Question

Determine whether the following sequence is geometric. If so, find the common ratio,

1.-3.9. - 27,...

Answer 1

Yes, the sequence is geometric

common ratio (r) = -3

Explanation:

Given:

• 
  `a_1=1`
• 
  `a_2=-3`
• 
  `a_3=9`
• 
  `a_4=-27`

If a sequence is geometric, common ratio
`r`:

`r=(a_4)/(a_3)=(a_3)/(a_2)=(a_2)/(a_1)`

Substituting the given values:

`\implies (a_4)/(a_3)=(-27)/(9)=-3`

`\implies (a_3)/(a_2)=(9)/(-3)=-3`

`\implies (a_2)/(a_1)=(-3)/(1)=-3`

Therefore, as

`(a_4)/(a_3)=(a_3)/(a_2)=(a_2)/(a_1)=-3`

the sequence is geometric with common ratio of -3