Question

A sequence is defined recursively by f(1)=6 and f(n)=f(n-1)+2n. Find f(4)

Answer 1

Since we have given the value of f(1) = 6 at n = 1, we proceed n = 2, 3 and 4 to reach f(4).
At n = 2,
f(2) = f(2 - 1) + 2(2)
f(2) = f(1) + 4
f(2) = 6 + 4
f(2) = 10

At n = 3,
f(3) = f(3 - 1) + 2(3)
f(3) = f(2) + 6
f(3) = 10 + 6
f(3) = 16

Notice that it follows the sequence: 6, 10, 16 by just adding 6. Thus,
f(4) = 16 + 6
f(4) = 22