Question

What is the explicit formula for the geometric sequence with this recursive formula?

Answer 1

Answer:

A

Step-by-step explanation:

The explicit formula for a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

The recursive formula gives a term in the sequence by multiplying the previous term by r

Given the recursive formula

a₁ = - 6

$a_{n}$ = $a_{n-1}$ ($\frac{1}{4}$ )

with r = $\frac{1}{4}$

Then explicit formula is

$a_{n}$ = - 6$(\frac{1}{4}) ^{n-1}$ → A