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?

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.

Answer 1

Answer:

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.

Step-by-step explanation: