Question

5) For the geometric sequence with the following terms, a8= 32 and a11= 256, find the ratio and then find a13

Answer 1

Using geometric sequence concepts, it is found that:

• The common ratio is of 2.

• The 13th term is of 1024.

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 is given by:

$a_n = a_mq^{n - m}$

Hence, considering the 8th and the 11th term, the common ratio is found as follows:

$a_{11} = a_8q^3$

$32q^3 = 256$

$q^3 = 8$

q = 2.

Then, considering the 11th term and the common ratio, the 13th term is given as follows:

$a_{13} = a_{11}q^2 = 256 \times 2^2 = 1024$

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

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