SOLUTION: I just don't even know what to say..................help!!!!!!!!!!!!!!!!! Given the following recursively defined sequence, find the fifth term. a_1 = -4 a_2 = -4 a(_n+2)= a(

Algebra ->  Sequences-and-series -> SOLUTION: I just don't even know what to say..................help!!!!!!!!!!!!!!!!! Given the following recursively defined sequence, find the fifth term. a_1 = -4 a_2 = -4 a(_n+2)= a(      Log On


   

Question 43317: I just don't even know what to say..................help!!!!!!!!!!!!!!!!!
Given the following recursively defined sequence, find the fifth term.
a_1 = -4
a_2 = -4
a(_n+2)= a(_n+1)-4a_n
a. 28
b. 764
c. -20
d. -308
e. None of the others

Found 2 solutions by fractalier, psbhowmick:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
This isn't as hard as you think...from
a_(n+2)= a_(n+1) - 4a_n
you merely plug in a_1 = -4 and a_2 = -4 to find a_3...
a_3 = -4 - 4(-4) = 12 now continue
a_4 = 12 - 4(-4) = 28
a_5 = 28 - 4(12) = -20
Choice C.

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D+=+-4
a%5B2%5D+=+-4

Now,
a%5Bn%2B2%5D+=+a%5Bn%2B1%5D+-+4a%5Bn%5D

When, n = 1,
a%5B1%2B2%5D+=+a%5B1%2B1%5D-4a%5B1%5D
or a%5B3%5D+=+a%5B2%5D-4a%5B1%5D
or a%5B3%5D+=+-4+-4%2A%28-4%29+=+12

When, n = 2,
a%5B2%2B2%5D+=+a%5B2%2B1%5D-4a%5B2%5D
or a%5B4%5D+=+a%5B3%5D-4a%5B2%5D
or a%5B4%5D+=+12+-4%2A%28-4%29+=+28

When, n = 3,
a%5B3%2B2%5D+=+a%5B3%2B1%5D-4a%5B3%5D
or a%5B5%5D+=+a%5B4%5D-4a%5B3%5D
or a%5B5%5D+=+28+-+4%2A12+=+-20

Hence, (c) is correct.