Question

Consider the following geometric sequence 2,6,18,54
what is the recursive and explicit formula?

Answer 1

recursive:
a(1)≈2
a(n)≈a(n-1)x3

explicit:
a(n)≈ 2(3)^n-1

Answer 2

Explanation:

The given geometric sequence is:

2,6,18,54

Here,
`a_(1)=2`,
`a_(2)=6`,
`a_(3)=18` and
`a_(4)=54`

Explicit formula is given as:
`a_(n)=a_(1)r^(n-1)`

Now,
`r=(a_(n+1))/(a_(n))`

=
`(6)/(2)=3`

Substituting in the above explicit formula, we have

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

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

Recursive formula is given as:
`a_(1)=2`,
`a_(n+1)=3a_(n)`.