Question

Find the missing terms in the following geometric sequence. -12,__,__, -324

Answer 1

y=ar^t

-324/-12=(ar^4)/(ar^1)

27=r^3

3=r

-12=a(3^1)

-12=3a

-4=a

y=-4(3^n)

y(2)=-36

y(3)=-108

Answer 2

The nth term for the geometric sequence is given by:

`a_n = a_1 \cdot r^(n-1)`

where,

`a_1` is the first term

r is the common ratio of the terms.

As per the statement:

Given the sequence

-12,__,__, -324

here,
`a_1 = -12` and
`a_4 = -324`

Solve for r:

By definition we have;

`a_4 = a_1 \cdot r^3`

⇒
`-324 = -12 \cdot r^3`

Divide both sides by -12 we have;

`27 = r^3`

⇒
`r = \sqrt[3]{27} =\sqrt[3]{3^3} = 3`

We have to find the missing terms
`a_2, a_3`

`a_2=a_1 \cdot r`

⇒
`a_2 = -12 \cdot 3 = -36`

`a_3=a_1 \cdot r^2`

⇒
`a_2 = -12 \cdot 3^2 = -12 \cdot 9 = -108`

therefore, the missing terms in the following geometric sequence is,

-12,_-36_,_-108_, -324