Question

If a sequence is defined recursively by f(0)= 3 and f(n + 1)= -f(n) +5 for n ≥ 0, then f(2) is equal to a) 2 b)3 c)5 d)8

Answer 1

Answer: B) 3

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f(0) = 3 is the given initial term
f(n+1) = -f(n)+5 is the recursive rule

Plug in n = 0 to find the next term
f(n+1) = -f(n)+5
f(0+1) = -f(0)+5 ... replace every n with 0
f(1) = -3+5 ... replace f(0) with 3
f(1) = 2

The second term is f(1) = 2

Then plug in n = 1 to find the next term after that
f(n+1) = -f(n)+5
f(1+1) = -f(1)+5 ... replace n with 1
f(2) = -2+5 ...... replace f(1) with 2
f(2) = 3

we stop here because we found the value for f(2)