Finding the next terms of an arithmetic sequence with whole numbers

---

---

Introduction

A sequence is a set or series of numbers that follow a certain rule.

For example −

1, 3, 5, 7 is a sequence of numbers that follow a rule: To find a number in this sequence we add 2 to the previous number.

An Arithmetic sequence is a series of numbers where each number is found by adding or subtracting a constant from the previous number.

The constant in an arithmetic sequence is known as the common difference d.

In general, we write an arithmetic sequence as follows

a, a + d, a + 2d , a + 3d, a + 4d

where, a is the first term and d is the common difference.

The rule for finding nth term of an arithmetic sequence

a_n = a + (n1)d

a_n is the n^th term, d is the common difference.

Example 1

The first three terms of an arithmetic sequence are 13, 18, and 23. Find the next two terms of this sequence.

Solution

Step 1:

Given the arithmetic sequence 13, 18 and 23. The common difference is

18 13 = 23 18 = 5 or d = 5

Step 2:

The next two terms in the sequence are 23 + 5 and 28 + 5 or 28 and 33

So the answer is 28 and 33

Example 2

The first three terms of an arithmetic sequence are 11, 4, and 3. Find the next two terms of this sequence.

Solution

Step 1:

Given the arithmetic sequence 11, 4 and 3. The common difference is

4 11 = 3 4 = 7 or d = 7

Step 2:

The next two terms in the sequence are 3 7 and 10 7 or 10 and 17

So the answer is 10 and 17