Question

The first 5 numbers of a sequence are shown below. Which of the following functions produces the sequence with n: {1, 2, ..., n} ?

27, 31, 35, 39, 43,...

A. f(n) = 23 - 4n
B. f(n) = 4n + 23
C. fin) = 27 - 4n
D. f(n) = 4n + 27

Answer 1

The correct function to produce the given sequence is D. f(n) = 4n + 27.

Step-by-step explanation:

The sequence provided is 27, 31, 35, 39, 43, and it appears to be an arithmetic sequence with a common difference of 4. In an arithmetic sequence, the general form of the nth term
`a_n` is given by
`\(a_n = a_1 + (n-1)`d, where
`a_1`is the first term and d is the common difference.

Comparing this with the given sequence, we can observe that the first term
`a_1` is 27, and the common difference d is 4. Therefore, the correct function is f(n) = 27 + 4(n-1), which simplifies to f(n) = 4n + 23.

However, the options provided are in a different format. To match the given options, we can rewrite f(n) = 4n + 23 as f(n) = 4n + 27 - 4. This is equivalent to f(n) = 4n + 27 - 4(1), which fits the form f(n) = 4n + 27 - 4n, matching option D.

Therefore, the correct choice is D.f(n) = 4n + 27, as it accurately represents the arithmetic sequence with a common difference of 4 and a starting term of 27.