Expert: Steve Holleran - 9/11/2007

Question
g(0)=1,g(1)=-1;if g(n)=g(n-1)+g(n-2)then find the value of g(6)?(please give me answer with explanation)

Answer
Hi Leela,

Okay, it looks like you are defining the terms in a sequence
by what's called a recursive rule.

The first two terms are given to you:

g(0) = 1   and g(1) = -1.

The equation g(n) = g(n-1) + g(n-2) tells you how to get the next terms.  It just says to get the following terms, add the two previous terms.  If you look  at the subscripts, compared to "n", n-1 is the one before it, and n-2 the one before that.  For example, if n = 2,

    g(2) = g(1) + g(0) = -1 + 1 = 0

then g(3) = g(2) + g(1) = 0 + (-1)= -1

    g(4) = g(3) + g(2) = -1 + 0 = -1

    g(5) = g(4) + g(3) = -1 + -1 = -2

    g(6) = g(5) + g(4) = -2 + -1 = -3.

Hope this helps out.

Steve Holleran