SOLUTION: 2. If a sequence is defined recursively by f(0)=2 and f(n+1)=-2f(n)+3 for n≥0 then f(2) is equal to A. -11 B. 1 C. 5 D. 17

Algebra ->  Sequences-and-series -> SOLUTION: 2. If a sequence is defined recursively by f(0)=2 and f(n+1)=-2f(n)+3 for n≥0 then f(2) is equal to A. -11 B. 1 C. 5 D. 17      Log On


   



Question 1049756: 2. If a sequence is defined recursively by f(0)=2 and f(n+1)=-2f(n)+3 for n≥0 then f(2) is equal to
A. -11
B. 1
C. 5
D. 17

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
f%280%29+=+2+ and
f%28n%2B1%29+=+-2f%28n%29+%2B+3+for n+%3E=+0,
here is the sequence for the first three numbers:

n+=+0:

f%280%2B1%29+=+-2+%2A+f%280%29+%2B+3
f%281%29+=+-2+%2A+2+%2B+3
f%281%29+=+-4+%2B+3
f%281%29+=+-1

n+=+1:

f%281%2B1%29+=+-2+%2A+f%281%29+%2B+3
f%282%29+=+-2+%2A%28+-1%29+%2B+3
f%282%29+=+2+%2B+3
f%282%29+=+5
n+=+2

f%283%29+=+-2+%2A+f%282%29+%2B+3
f%283%29+=+-2+%2A+5+%2B+3
f%283%29+=+-10+%2B+3
f%283%29+=+-7

so, f%282%29 is equal to 5 and your answer is C.