Question

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

Answer 1

Answer:

Option C

Step-by-step explanation:

Given is a geometric sequence.

The recursive formula is given as

$a_n = \frac{1}{3} a_{n-1}$

Hence ratio of nth term to n-1th term

=$\frac{a_n}{a_{n-1} } =\frac{1}{3}$

$r=\frac{1}{3}$

I term = $a_1=-7$

Hence explicit formula is

$a_n = -7(\frac{1}{3} )^{n-1}$

Option C is right

Answer 2

C

generate the first few terms using the recursive formula

$a_{2}$ = - 7 × $\frac{1}{3}$ = - $\frac{7}{3}$

$a_{3}$ = - $\frac{7}{3}$ × $\frac{1}{3}$ = - $\frac{7}{9}$

$a_{4}$ = - $\frac{7}{9}$ × $\frac{1}{3}$ = - $\frac{7}{27}$

r = $a_{2}$ / $a_{1}$ = $\frac{1}{3}$

the n th term formula (explicit ) for a geometric sequence is

$a_{n}$ = $a_{1}$$r^{n-1}$ = - 7($\frac{1}{3}$)^(n - 1)