Question

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

Answer 1

Answer:

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

Answer 2

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