Question

What is the recursive formula when given the explicit formula for thefollowing geometric sequence?2n = 12(33)^-1O A. a₁ = 12, a = -33an-1OB. a₁ = 12, a = 33an-1OC. a₁ = 33, an = 12am-1OD. a₁ = 33, a = -12am-1

Answer 1

Given that the explicit formula for GP is

$a_n=12(33)^{n-1}$

Explanation -

The general explicit formula for GP is

$\begin{gathered} a_n=ar^{n-1} \\ where\text{ a=first term and r = common ratio} \end{gathered}$

and the recursive formula for that GP is given as

$a_n=a_{n-1}\times r$

Comparing the general formula with the given explicit formula we have

$a=12\text{ and r = 33}$

So the required recursive formula will be a

$a_n=33\times a_{n-1}$

So option B is correct.

The final answers are, the first term is a = 12 and the recursive formula is $a_n=33a_{n-1}$