Question

Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2.

Answer 1

The given sequence is

`a_(1)=2 \\ a_(n+1)=-4a_(n)+2`

Write the first 4 terms.
When n=1, obtain
a₁ = 2
When n=2, obtain
a₂ = -4a₁ + 2
= -4(2) + 2 = -8 + 2
= -6
When n=3, obtain
a₃ = -4a₂ + 2
= -4(-6) + 2 = 24 + 2
= 26
When n=4, obtain
a₄ = -4a₃ + 2
= -4(26) + 2 = -104 + 2
= -102

Answer: a₄ = -102