Question

ANSWER ASAP!
what is the value of a₁₇ if a₁₃=26 and the recursive form of a geometric sequence is aₙ=1/2aₙ₋₁


please answer with atleast some detail

Answer 1

The 17th term of the geometric sequence is:

$a_{17} = \frac{13}{8}$

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

$a_n = a_1q^{n-1}$

In which $a_1$ is the first term.

As a function of the mth term, the nth term can also be given as follows:

$a_n = a_mq^{n - m}$

In this problem, we have that:

$a_{13} = 26, q = \frac{1}{2}$

Hence the 17th term is:

$a_{17} = a_{13}q^{4}$

$a_{17} = 26 \times \frac{1}{16}$

$a_{17} = \frac{13}{8}$

More can be learned about geometric sequences at https://brainly.com/question/11847927

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