Algebra 2 sequences

Question

Find the 4th term of the sequend in which a₁=2 and a_n= -4a_n-1+2

Answer 1

For this type of problem, you have to do the iterations.

a₁ = 2

a₂ = -4a_2-1 + 2 = -4a₁ + 2 = -4(2) + 2 = -6

a₃ = -4a_3-1 + 2 ...

Keep doing the iterations until you reach the term you want.

Answer 2

April, let's do this question!

The n^th term is related to the (n -1)^th term by a plus so this is an arithmetic series.

For the general arithmetic series, a_n = a₁ + (n - 1)d

=> -4a_n-1 + 2 = 2 + (n - 1)d [Now let n = 2 (so we get a₁ on the left, which = 2

=> -4a₁ + 2 = 2 + (2 - 1)d

=> -4(2) + 2 = 2 + d

=> d = -8

∴ the 4th term, a₄ = a₁ + (4 - 1)d

= 2 + 3(-8)

= -22

Done!