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

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