Question

The first term of a geometric sequence is -2 and the common ratio is 3, What is the sixth term of the sequence?

Also, Write the Recursive Rule fo the seqeunce from above ^

Answer 1

a₆ = - 486

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

Here a₁ = - 2 and r = 3 , then

a₆ = - 2
`(3)^(5)` = - 2 × 243 = - 486

The recursive rule allows a term in the sequence to be found by multiplying the previous term by the common ratio, that is

`a_(n)` = 3
`a_(n-1)` with a₁ = - 2