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.

Question

Gavin Cabrera

Mathematics

14 January, 01:13

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.

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Answers (1)

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Daphne Wall · Answer 1

The only correct answer is 'C', the common difference is 10, so the function is f (n + 1) = f (n) + 10 where f (1) = 14. The first number of the sequence is 14 so f (1) is 14 and each number in the sequence is the previous number + 10. The first number is 14 so the second number, or f (1+1) is 14 + 10, making the second number in the sequence 24 and so on, adding 10 each time to the number before.