f (n + 1) = f(n) – 5 is the recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1
Solution:
Given that,
f(1) = 6 and n ≥ 1
Given sequence is 6, 1, -4, -9, -14
Let us first analyse the logic used in this sequence
6 - 5 = 1
1 - 5 = -4
-4 - 5 = -9
-9 - 5 = -14
Thus the next terms in sequence are obtained by subtracting 5 from previous term
Thus a recursive formula can be formed as:
f (n + 1) = f(n) – 5
Where "n" is the nth term
Let us check our recursive formula:
f(1+ 1) = f(1) - 5
f(2) = f(1) - 5
f(2) = 6 - 5 = 1
Thus we have got f(2) = 1 which is correct as per given sequence