SOLUTION: What is the closed linear form for this sequence given a1 = 14 and an + 1 = an - 2? A) an = 16 + 2n B) an = 16 - 2n C) an = 14 + 2n D) an = 14 - 2n

Algebra ->  Equations -> SOLUTION: What is the closed linear form for this sequence given a1 = 14 and an + 1 = an - 2? A) an = 16 + 2n B) an = 16 - 2n C) an = 14 + 2n D) an = 14 - 2n      Log On


   

Question 1133525: What is the closed linear form for this sequence given a1 = 14 and an + 1 = an - 2?
A) an = 16 + 2n
B) an = 16 - 2n
C) an = 14 + 2n
D) an = 14 - 2n
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
a%5B1%5D+=+14
and
a%5Bn%5D+%2B+1+=+a%5Bn%5D+-+2


since a%5Bn%5D+%2B+1+=+a%5Bn%5D+-+2 we can see that each term successive decreases by +2
y+=+-2x+%2B+b+

if a%5B1%5D+=+14 it means when x+=+1, y+=+14 so b is
14+=+-2+%2B+b
b=16 and equation is

y+=+-2x+%2B+16+

answer:
B) a%5Bn%5D+=+16+-+2n