Question

what is the nth term of the geometric sequence that has a common ratio of 6 and 24 as its third term?

Answer 1

The nth term of the series is

`a_n=(2)/(3)\cdot 6^(n-1)`

Explanation:

Given: Third term = 24 and r = 6

We are given third term and common ratio of geometric series.

Formula:

`a_n=a\cdot r^(n-1)`

For third term, n=3 and r=6

`a_3=a\cdot 6^(3-1)`

`24=a\cdot 36`

`a=(2)/(3)`

We need to find nth term of the series

`a_n=(2)/(3)\cdot 6^(n-1)`

Hence, The nth term of the series is
`a_n=(2)/(3)\cdot 6^(n-1)`

Answer 2

Common ratio, r= 6
3rd term=24
Finding first term=
24=a
`6^(2)`
24=36a
a=24/36
a=2/3
nth term=
`2/3(6)^(n-1)`