Question

Find the first four terms of the recursive sequence defined by the following formula: an = an-1 4 where a4 = 2 1 4 , , , 2 1 4.

Answer 1

The first four-term of the sequence is found by the given equation $a_{n-1} = 4a_n$ is given as 144, 36, 9, and 9/4.

What is a sequence?

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The given equation will be

$\rm a_n = \dfrac{a_{n-1}}{4} \\\\a_{n-1} = 4a_n$

And

$a_4 = 2 \dfrac{1}{4} = \dfrac{9}{4}$

For n = 4, we have

$\rm a_{4-1} = 4a_4\\\\a_3 \ \ \ = 4*\dfrac{9}{4} \\\\ a_3 \ \ \ = 9$

For n = 3, we have

$\rm a_{3-1} = 4a_3\\\\a_2 \ \ \ = 4*9 \\\\ a_2 \ \ \ = 36$

For n = 2, we have

$\rm a_{2-1} = 4a_2\\\\a_1 \ \ \ = 4*36 \\\\ a_1 \ \ \ = 144$

More about the sequence link is given below.

brainly.com/question/21961097