Question

The recursive rule is f(1) = 99; f(n)=f(n-1)+4 and one of the terms is 119. What position is 119 in for this sequence?

Answer 1

f(1) = 99
f(2) = f(1) + 4 = 99 + 4 = 103

nth term of an arithmetic sequence is given by Tn = a + (n - 1)d; where Tn = 119, a = 99 and d = 4

119 = 99 + (n - 1)4 = 99 + 4n - 4 = 95 + 4n
4n = 119 - 95 = 24
n = 24/4 = 6

Therefore, 119 is in the 6th position.