Question

Consider the first three terms of the sequence below. 7,13,19,25 Complete a recursively-defined function to describe this sequence. f(1) = _____ f(n) = f(n - 1) · ___, for n ≥ 2 The next term in the sequence is ____.

Answer 1

The first term in the sequence is 7, and the recursively-defined function is f(1) = 7 and f(n) = f(n - 1) + 6 for n ≥ 2. The next term after 25 in the sequence is 31.

Step-by-step explanation:

To find the recursively-defined function for the sequence 7, 13, 19, 25,..., we first identify the pattern between consecutive terms. We see that each term increases by 6 when compared to the previous term.

Thus, the recursive function has a base case of f(1) = 7 and a recursive step where each term is 6 more than the previous term, which gives us f(n) = f(n - 1) + 6 for n ≥ 2.

The next term after 25 in the sequence is 25 + 6, which equals 31.