Question

if f(1) = -5 and f(n) = f(n-1) +7, find the first four terms and the common difference of the sequence

Answer 1

- 5, 2, 9, 16 and d = + 7

Explanation:

to obtain the first four terms substitute n = 2, 3, 4 into the recursive formula

f(1) = - 5 ← given

f(2) = f(1) + 7 = - 5 + 7 = 2

f(3) = f(2) + 7 = 2 + 7 = 9

f(4) = f(3) + 7 = 9 + 7 = 16

common difference d = 16 - 9 = 9 - 2 = 2 - (- 5) = 7