Find the first six terms of the sequence in which f (1) = 4 and f (n) = f (n-1) + (n+6), n>1

The first 6 terms are 4, 12, 21, 31, 42 and 54

Step-by-step explanation:

Step 1: Given f (n) = f (n-1) + (n+6) and f (1). Find the 6 terms by substituting in f (n)

⇒ f (1) = 4

⇒ f (2) = f (1) + (2+6) = 4 + 8 = 12

⇒ f (3) = f (2) + (3+6) = 12 + 9 = 21

⇒ f (4) = f (3) + (4+6) = 21 + 10 = 31

⇒ f (5) = f (4) + (5+6) = 31 + 11 = 42

⇒ f (6) = f (5) + (6+6) = 42 + 12 = 54