Question

Question #1f6de

Answer 1

`a_4=a_3xx6 " "=" " 144xx6 " "=" " 864`

`a_5=a_5xx6" "=" "864xx6" "=" "5184`

`a_6=a_5xx6" "=" "5184xx6" "=" " 31122`

Explanation:

Let the term count be `i`
Let the ith term be `a_i`

So we have:
`i=1->a_i =a_1=4`
`i=2->a_i=a_2=24`
`i=3->a_i=a_3=144`

The question states this is a geometric sequence.

Let the expression for the term be `a_ir^n`
Where `r` is the common ratio and `n` is some variant (function) of `i`

`color(brown)("Determine the value of "r)`

`24/4= 6`

`144/24=6`

Thus `r=6`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Determine the next three terms")`

The last known term is `a_3=144`

so we have:

`a_4=a_3xx6 " "=" " 144xx6 " "=" " 864`

`a_5=a_5xx6" "=" "864xx6" "=" "5184`

`a_6=a_5xx6" "=" "5184xx6" "=" " 31122`