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