Question

1. Find the 6th term in the geometric sequence where a1= 2 and r= 3

2. Find the 9th term in the geometric sequence where a1= 1/3 and r= 3

Answer 1

486 and 2187

Explanation:

the nth term of a geometric sequence is

`a_(n)` = a₁ ×
`r^(n-1)`

where a₁ is the first term and r the common ratio

(1)

here a₁ = 2 and r = 3 , then

a₆ = 2 ×
`3^(5)` = 2 × 243 = 486

(2)

here a₁ =
`(1)/(3)` and r = 3 , then

a₉ =
`(1)/(3)` ×
`3^(8)` =
`(1)/(3)` × 6561 = 2187