Question

What is the explicit rule for the sequence 3, –6, 9, –18, 36, ...?

A. an =2(–3)n–1

B. an =3(2)n–1

C. an =3(–2)n

D. an =3(–2)n–1

Answer 1

The answer would be C.

Answer 2

D.
`a_n=3(-2)^(n-1)`

Explanation:

We have been given a sequence 3, –6, 9, –18, 36, ... . We are asked to find an explicit rule for our given sequence.

We can see that our given sequence is geometric as each difference between two consecutive terms is not equal.

We know that a geometric sequence is in form
`a_n=a_1(r)^(n-1)`, where,

`a_n` = nth term of sequence,

`a_1` = 1st term of sequence,

r = Common ratio

n = Number of terms in sequence.

First of all, we will find common ratio of given sequence by dividing any term of sequence by it previous term as:

`r=(-6)/(3)=-2`

We can see that 1st term of our given sequence is 3.

Upon substituting our given values in above formula, we will get:

`a_n=3(-2)^(n-1)`

Therefore, our required formula is
`a_n=3(-2)^(n-1)` and option D is the correct choice.