Question

4. What is the rule of the nth term of the geometric sequence with
`a_(4)` = -18 and the common ratio r = 2?

a.
`a_(n)=2.25(2)^(n-1)`

b.
`a_(n)=2(2.25)^(n-1)`

c.
`a_(n)=2(2.25)^(n-1)`

d.
`a_(n)=-2.25(2)^(n-1)`

e.
`a_(n)=-2.25(-2)^(n-1)`

Answer 1

`\text{d.}\quad a_n=-2.25(2)^(n-1)`

Explanation:

The common ratio is given as 2, so the base of any exponential must be 2 (not -2 or 2.25). The 4th term is negative, so the initial value must be negative (since the multiplying factor is positive). The only selection matching these requirements is d.

You know the general term is ...

... an = a1·r^(n-1)

so the 4th term is

... -18 = a1·2^(4-1) = 8·a1

Then the first term is ...

... a1 = -18/8 = -2.25 . . . . . confirms our choice of answer d.