Which recursive formula can be used to generate the sequence below, where f (1) = 6 and n ≥ 1?

6, 1, - 4, - 9, - 14, ...

optian 2

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