Question

Please answer 4 Complete a sequence and find the growth factor

Answer 1

Given:

The given sequence is a geometric sequence.

`\text{ \_\_\_\_, \_\_\_\_\_\_, 36, -108, \_\_\_\_}`

Required:

We need to find the missing terms.

Step-by-step explanation:

We know that the geometric sequence has a common ratio.

Divide -108 by 36 to find the common ratio r.

`r=-(108)/(36)=-3`

The third term is 36 and the common ratio is (-3).

Consider the nth term equation.

`a_n=ar^(n-1)`

Substitute n=3 in the equation.

`a_3=ar^(3-1)=ar^2`
`Substitute\text{ }a_3=36\text{ and t =-3 in the equation.}`
`36=a(-3)^2`
`36=a(9)`

Divide both sides by 9.

`(36)/(9)=(9a)/(9)`
`4=a`

We get the first term =4.

Multiply 4 by (-3) to get the second term.

`a_2=4*(-3)=-12`

The second term is -12.

The fourth term is -108.

Multiply -108 by -3 to get the fifth term.

`a_5=(-108)*(-3)`
`a_5=324`

Final answer:

The required sequence is

`4,-12,36,-108,324`

The growth factor is -3.