Question

A sequence is recursively defined by f(1)=3,f(n)=2* f(n-1) for n >=2. Write the equation for the nth term

Answer 1

Given:

`f(1)=3,f(n)=2* f(n-1)` ...(i)

For
`n\geq 2`.

To find:

The nth term for the given recursive formula.

Solution:

The given recursive formula is of the form of

`f(n)=r* f(n-1)` ...(ii)

It is the recursive formula of a GP, where r is common ratio.

On comparing (i) and (ii), we get

`r=2`

Now,

First term:
`a=f(1)=3`

Common difference:
`r=2`

nth term of a GP is

`f(n)=ar^(n-1)`

Putting a=3 and r=2, we get

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

Therefore, the equation for the nth term is
`f(n)=3(2)^(n-1)`.