Question

One term of a geometric sequence is a3= 12. the common ratio is r= 2. write an explicit rule for the nth term.

Answer 1

`a_(n)` = 3
`(2)^(n-1)`

Explanation:

the nth term ( explicit rule ) for a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

we require to find a₁

given a₃ = 12 , then

a₁ (r)² = 12

a₁ × 2² = 12

4a₁ = 12 ( divide both sides by 4 )

a₁ = 3

then explicit formula is

`a_(n)` = 3
`(2)^(n-1)`