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.

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:

          .....[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

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: