Question

If I know a5 = -48 and r = 2 in a geometric sequence, how do i find the 8th term and explicit formula? How can I calculate a1?

Answer 1

Data:
a5 = - 48
Being r = q = 2
a1 = ?
a8 = ?
n (Number of terms)

Solving:

Formula (geometric progression)


`a_(n) = a_(1) *q^(n-1)`

We have:
find the 1th (a1)


`a_(n) = a_(1) *q^(n-1)`

`a_(5) = a_(1) *2^(5-1)`

`-48 = a_(1) *2^(4)`

`-48 = a_(1) *16`

`16a_(1) = -48`

`a_(1) = (-48)/(16)`

`\boxed{a_(1) =-3}`

find the 8th (a8)


`a_(n) = a_(1) *q^(n-1)`

`a_(8) = -3 *2^(8-1)`

`a_(8)= -3 *2^(7)`

`a_(8)= -3 *128`

`\boxed{a_(8) =-384}`

Answer:

`\boxed{a_(1) = -3}`

`\boxed{a_(8) = -384}`