Finding the sum of an arithmetic sequence might seem hard at first, but once you understand it, it gets easier. Let’s break it down into simple parts.

What is an Arithmetic Sequence?

An arithmetic sequence is a list of numbers where each number is the same distance apart from the next one. This distance is called the common difference.

For example, in the sequence 2, 5, 8, 11, the common difference is 3, because you add 3 each time to get the next number.

The Formula

To find the sum of the first n numbers in an arithmetic sequence, you can use this easy formula:

$$S_n = \frac{n}{2} \times (a + l)$$

Here’s what the letters mean:

• $n$ = how many numbers you have
• $a$ = the first number
• $l$ = the last number

If you don’t know the last number, you can use this other formula:

$$S_n = \frac{n}{2} \times (2a + (n-1)d)$$

In this formula, $d$ is the common difference.

Simple Steps to Find the Sum

1. Identify the terms: First, figure out your first number ($a$) and how many numbers there are ($n$).

2. Find the last term: If you can find the last number ($l$) by counting or solving, it will help a lot.

3. Use the formula: Just put your numbers into one of the formulas above, and you will get your sum!

Keep Practicing

The more you practice with different sequences, the better you will get! Each sequence is unique, but remember, using the right formula will help you find the answer quickly every time!