Question

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

Answer 1

From 14 to 24 is 10; from 24 to 34 is 10, and so on, so the common difference is 10.  

f(1) = 14
f(2) = 24 = 14 + (2-1)(10) = 14 + (n-1)(10)

So f(n) = 14 + (n-1)(10)

Check:  Does f(4) come out to 44, as we expected?
              Does 14 + (4-1)(10) = 44?  Yes.

Answer 2

Answer:

Option C is correct

The common difference is 10,

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

Step-by-step explanation:

The recursive function for the arithmetic sequence is given by:

$f(n+1) = f(n)+d$           .....[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;

$f(n+1) = f(n) + 10$

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

$f(n+1) = f(n) + 10$ and f(1) = 10