Question 974411: if f(1)=3 and f(n)= -2f(n-1) +1, then f(5) = ???
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! f(1)=3 is given
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f(n)= -2f(n-1) +1
f(2)= -2f(2-1) +1 ... replace n with 2
f(2)= -2f(1) +1
f(2)= -2*3 +1 ... replace f(1) with 3
f(2) = -5
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f(n)= -2f(n-1) +1
f(3)= -2f(3-1) +1 ... replace n with 3
f(3)= -2f(2) +1
f(3)= -2*(-5) +1 ... replace f(2) with -5
f(3) = 11
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f(n)= -2f(n-1) +1
f(4)= -2f(4-1) +1 ... replace n with 4
f(4)= -2f(3) +1
f(4)= -2*(11) +1 ... replace f(3) with 11
f(4) = -21
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f(n)= -2f(n-1) +1
f(5)= -2f(5-1) +1 ... replace n with 5
f(5)= -2f(4) +1
f(5)= -2*(-21) +1 ... replace f(4) with -21
f(5) = 43
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Summary:
f(1) = 3
f(2) = -5
f(3) = 11
f(4) = -20
f(5) = 43
Notice how we had to build our way up to get to f(5). We started with f(1) which was given. Then we used that to find f(2). Then we used f(2) to find f(3), etc etc until got to f(5). This is a recursive function. Each term is found by using the previous term (except for the given f(1) term). It isn't so bad for small values of n, but gets somewhat tedious to do by hand for large values of n.
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