Question

The fifth term of a geometric sequence is 781.25. Each term of the sequence is 1/5 of the value of the following term. Which recursive formula represents the situation?
Answer choices are in the image attached.

Answer 1

The recursive formula of the geometric sequence is $a_{n} = 5a_{n-1}$ and a1 = 1.25

How to determine the recursive formula?

The given parameters are:

Fifth term = 781.25

Term = 1/5 * following term

The second parameter above means that:

$a_n = \frac{1}{5} * a_{n+ 1}$

Multiply both sides by 5

$a_{n+1} = 5a_n$

Remove 1 from the terms

$a_{n} = 5a_{n-1}$

Using the formula $a_n = \frac{1}{5} * a_{n+ 1}$, we have the first term to be:

$a_1 = \frac 15 * a_2$

$a_2 = \frac 15 * a_3$

$a_3 = \frac 15 * a_4$

$a_4 = \frac 15 * a_5 = \frac 15 * 781.25 = 156.25$

So, we have:

$a_3 = \frac 15 * 156.25 = 31.25$

$a_2 = \frac 15 * 31.25 = 6.25$

$a_1 = \frac 15 * 6.25 = 1.25$

Hence, the recursive formula is $a_{n} = 5a_{n-1}$ and a1 = 1.25

Read more about recursive sequence at:

brainly.com/question/1275192

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