Question

Find the first six terms of the sequence.

a1 = -7, an = 2 • an-1

Answer 1

The first 6 terms are -7,-14,-28,-56,-112,-224

Explanation:

The given sequence is defined recursively by:

`a_1=-7` and
`a_n=2(a_(n-1))`

When n=2

`a_2=2(a_(2-1))`

`a_2=2(a_(1))`

`a_2=2(-7)=-14`

When n=3

`a_3=2(a_(3-1))`

`a_3=2(a_(2))`

`a_3=2(-14)=-28`

When n=4

`a_4=2(a_(4-1))`

`a_4=2(a_(3))`

`a_4=2(-28)=-56`

When n=5

`a_5=2(a_(5-1))`

`a_5=2(a_(4))`

`a_5=2(-56)=-112`

When n=6

`a_6=2(a_(6-1))`

`a_6=2(a_(5))`

`a_6=2(-112)=-224`

The first 6 terms are -7,-14,-28,-56,-112,-224