SOLUTION: Special Sequences help? 1. Find the 4th term if the sequence in which a1 = 2 and an+1 = -4an + 2. I keep getting -128 as the answer. This is my work. a1 = 2 a2 = -8 + 2 = -6 a

Question 1005816: Special Sequences help?
1. Find the 4th term if the sequence in which a1 = 2 and an+1 = -4an + 2.
I keep getting -128 as the answer. This is my work.
a1 = 2
a2 = -8 + 2 = -6
a3 = -32 + 2 = - 30
a4 = -120 + 2 = -128

Please help! Thank you so much!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm assuming the sequence rule is

a1 = 2
a(n+1) = -4*a(n) + 2

In words: to find the next term, multiply the previous term by -4 and then add 2.
--------------------------------------------

If my assumption above is correct, then you made a mistake when you computed a3.

a1 = 2
------------------
a2 = -4*(a1) + 2
a2 = -4*(2) + 2
a2 = -8 + 2
a2 = -6
------------------
a3 = -4*(a2) + 2
a3 = -4*(-6) + 2 <--- You made a mistake on this step
a3 = 24 + 2
a3 = 26
------------------
a4 = -4*(a3) + 2
a4 = -4*(26) + 2
a4 = -104 + 2
a4 = -102

Final Answer: -102
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