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

Given:

        ...(i)

For .

To find:

The nth term for the given recursive formula.

Solution:

The given recursive formula is of the form of

           ...(ii)

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

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

Now,

First term:

Common difference:

nth term of a GP is

Putting a=3 and r=2, we get

Therefore, the equation for the nth term is .

the radius is 2 times the diameter.

step-by-step explanation: