Question

Find the first six terms of the sequence. a1 = -6, an = 4 • an-1

Answer 1

each term after the first is 4 times the previous one, so second term is
-6*4 = -24

first 6 terms are -6,-24, -96, -384, -1536, -6144

Answer 2

The first six terms of the sequence are -6, -24, -96, -384, -1536 and -6144.

Explanation:

Given information :
`a_1=-6,a_n=4\cdot a_(n-1)`.

It means the first term of the sequence is -6 and recursive formula is

`a_n=4\cdot a_(n-1)`

Substitute n=2, to find the second term.

`a_2=4\cdot a_(2-1)=4\cdot a_(1)=4\cdot (-6)=-24`

Substitute n=3, to find the third term.

`a_3=4\cdot a_(3-1)=4\cdot a_(2)=4\cdot (-24)=-96`

Substitute n=4, to find the 4th term.

`a_4=4\cdot a_(4-1)=4\cdot a_(3)=4\cdot (-96)=-384`

Substitute n=5, to find the 5th term.

`a_5=4\cdot a_(5-1)=4\cdot a_(4)=4\cdot (-384)=-1536`

Substitute n=6, to find the 6th term.

`a_6=4\cdot a_(6-1)=4\cdot a_(5)=4\cdot (-1536)=-6144`

Therefore the first six terms of the sequence are -6, -24, -96, -384, -1536 and -6144.