Question

Find the next 3 terms in the geometric sequence -36, 6, -1, 1/6, ...

Answer 1

we are given

geometric sequence -36, 6, -1, 1/6, ...

first term is -36

`a_1=-36`

now, we can find common ratio

`r=(6)/(-36)`

`r=-(1)/(6)`

now, we can find nth term

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

now, we can plug values

and we get

`a_n=36(-(1)/(6))^(n-1)`

now, we can find 5th term , 6th term, 7th term

fifth term:

`a_5=36(-(1)/(6))^(4)`

`a_5=(1)/(36)`

sixth term:

`a_6=36(-(1)/(6))^(5)`

`a_6=-(1)/(216)`

seventh term:

`a_7=36(-(1)/(6))^(6)`

`a_7=(1)/(1296)`

so, next terms are

`a_5=(1)/(36)` ,
`a_6=-(1)/(216)`

,
`a_7=(1)/(1296)`.............Answer