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