The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ...

Which statement describes the recursive function used to generate the sequence?

The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14.
The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10.
The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.

Option C is correct

Step-by-step explanation:

The common difference is 10,

So,  the function is f(n + 1) = f(n) + 10 , where f(1) = 14

The recursive function for the arithmetic sequence is given by:

          [1]

where d is the common difference of the two consecutive terms.

Given the arithmetic sequence :

14, 24, 34, 44, 54,

First term f(1) = 14

Common difference(d) = 10

Since,

24 -14 = 10

34-24 = 10

44-34 = 10 and so on

Substitute d = 4 in [1], we have;

Therefore, the recursive function used to generate the sequence is,

and f(1) = 10