Question

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

Answer 1

f(2) = 3

Explanation:

We are given:

f(0) = 3

and

f(n+1) = -f(n) + 5

We have to find the value of f(2). In order to find f(2) we first have to find f(1)

f(n + 1) = - f(n) + 5

Using n = 0, we get:

f(0 + 1) = - f(0) + 5

f(1) = -f(0) + 5 Using the value of f(0), we get

f(1) = -3 + 5 = 2

Now using n = 1 in the function, we get:

f(1 + 1) = - f(1) + 5 Using the value of f(1), we get

f(2) = -2+ 5

f(2) = 3

Thus the value of f(2) will be 3