Question

Which of the following best defines the sequence shown?
8, 24, 72, 216, ...
​

Answer 1

Option (2)

Explanation:

Given sequence is,

8, 24, 72, 216........

1st term of the sequence 'a' = 8

Ratio of 2nd and 1st term =
`(24)/(8)=3`

Ratio of 3rd and 2nd term =
`(72)/(24)=3`

There is a common ratio of 'r' = 3 in each successive and previous term.

Therefore, it's a geometric sequence.

Since, nth term of a geometric sequence is given by,

`T_n=a(r)^(n-1)`

Therefore, function representing the geometric sequence is,

f(n) =
`f(n)=8(3)^(n-1)`

Option (2) is the answer.