Question

Rewrlte the following sequence using a recursive form ula: aɴ=6+2(n-1)

Answer 1

The recursive formula for the sequence a_n = 6 + 2(n-1) is a_n = a_(n-1) + 2 with the base case a_1 = 6. Each term is 2 more than the previous term.

Step-by-step explanation:

To rewrite the sequence a_n = 6 + 2(n-1) using a recursive formula, we first need to express the term a_n in relation to its predecessor, a_(n-1). To find a relationship between consecutive terms, we can calculate the difference between two consecutive terms:

a_n - a_(n-1) = [6 + 2(n-1)] - [6 + 2(n-2)]
= 6 + 2n - 2 - 6 - 2n + 4
= 2.

This means that each term is 2 more than the previous term. Now, we set our base case. The first term is a_1 = 6 (when n=1). We have the recursive relationship: a_n = a_(n-1) + 2, with the base case a_1 = 6.

A recursive sequence formula is comprised of the base case and the recursive step:

• Base case: a_1 = 6
• Recursive step: a_n = a_(n-1) + 2 for n > 1