Question

Find an explicit rule for the nth term of the sequence. 3, -12, 48, -192, ...

Answer 1

Hello,

`u_(1)=3`

`u_(2)=3*(-4)`

`u_(3)=3*(-4)^2`


`u_(n)=3*(-4)^(n-1)`

Answer 2

Answer:
`a_n=3(-4)^(n-1)`

Explanation:

Given sequence :
`3, -12, 48, -192, ...`

Here, First term
`a_1=3`

Second term
`a_2=-12`

and Ratio=
`r=(a_2)/(a_1)=(-12)/(3)=-4`

Third term
`a_3=48`

Ratio=
`r=(a_3)/(a_2)=(48)/(-12)=-4`

Fourth term
`a_4=-192`

Ratio=
`r=(a_4)/(a_3)=(-192)/(48)=-4`

Thus, the given sequence is geometric sequence with the common ratio r = -4.

The explicit rule for for the nth term in geometric sequence is given by

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

Then the explicit rule for the nth term of the given sequence will be :-

`a_n=3(-4)^(n-1)`