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.
Accepted Solution
A:
Answer:Option C is correctThe common difference is 10, So, the function is f(n + 1) = f(n) + 10 , where f(1) = 14Step-by-step explanation:The recursive function for the arithmetic sequence is given by:[tex]f(n+1) = f(n)+d[/tex] .....[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) = 14Common difference(d) = 10Since, 24 -14 = 1034-24 = 1044-34 = 10 and so on....Substitute d = 4 in [1], we have;[tex]f(n+1) = f(n) + 10[/tex]Therefore, the recursive function used to generate the sequence is,[tex]f(n+1) = f(n) + 10[/tex] and f(1) = 10