Understanding a Recursive Sequence Formula

The problem gives us a sequence and explains that each term of the sequence is formed by taking

the previous term and adding a number that follows a fixed pattern. Let’s analyze the

description step by step. The first term has a value of 1. The second term

is the first term plus 1. The third term is the second term plus 2.

The fourth term is the third term plus 3. And so on. Each term is obtained

by adding a certain number to the previous term, and that number happens to be “the

index minus 1.” In other words, the k-th term equals the (k−1)-th term plus (k−1).

With this description, we can write a recursive relation: The first term a₁ is 1.