Mastering the Sequence: Finding the nth Term

A beginner’s guide to solving sequence problems in Java

Photo by Thomas Tucker on Unsplash

In this article, we’ll focus on finding the nth term of a sequence with the first six terms given. Specifically, we’ll explore a sequence with the following first six terms: 2, 6, 13, 23, 36, 52. By the end of this guide, you’ll be able to write a function that calculates the nth term of this sequence. Let’s get started!

Step 1: Understanding the Problem

Let’s make sure we understand the problem. We need to find a function that takes an integer n as input and returns the nth term of the given sequence. For example, if n is 1, the function should return 2. If n is 2, the function should return 6, and so on.

Step 2: Analyzing the Sequence

To find the pattern in the sequence, let’s examine the differences between consecutive terms:

• The difference between the 2nd and 1st terms is 6–2 = 4.
• The difference between the 3rd and 2nd terms is 13–6 = 7.
• The difference between the 4th and 3rd terms is 23–13 = 10.
• The difference between the 5th and 4th terms is 36–23 = 13.
• The difference between the 6th and 5th terms is…