Arithmetic Progression Examples
Example 1: Find the AP if the first term is 15 and the common difference is 4.
Solution:
As we know,
a, a + d, a + 2d, a + 3d, a + 4d, …
Here, a = 15 and d = 4
= 15, (15 + 4), (15 + 2 × 4), (15 + 3 × 4), (15 + 4 × 4),
= 15, 19, (15 + 8), (15 + 12), (15 + 16), …
= 15, 19, 23, 27, 31, …and so on.
So the AP is 15, 19, 23, 27, 31…
Example 2: Find the 20th term for the given AP: 3, 5, 7, 9, …
Solution:
Given, 3, 5, 7, 9, 11……
Here,
a = 3, d = 5 – 3 = 2, n = 20
an = a + (n − 1)d
a20 = 3 + (20− 1)2
a20 = 3 + 38
a20 = 41
Here 20th term is a20 = 41
Example 3: Find the sum of the first 20 multiples of 5.
Solution:
First 20 multiples of 5 are 5, 10, 15, … 100.
Here, it is clear that the sequence formed is an arithmetic sequence where,
a = 5, d = 5, an = 100, n = 20.
Sn = n/2 [2a + (n − 1) d]
Sn = 20/2 [2 × 5 + (20 − 1)5]
Sn = 10 [10 + 95]
Sn = 1050
Arithmetic Progression
Arithmetic progression, also known as A.P. is a sequence in mathematics where the difference between the two consecutive terms is a constant. The constant is known as the common difference. The arithmetic progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
In this article, we will learn about Arithmetic Progression Definition, Arithmetic Progression Formulas, related examples and others in detail.
Table of Content
- What is Arithmetic Progression?
- Notations in Arithmetic Progression
- Common Difference of Arithmetic Progression
- First Term of Arithmetic Progression
- Nth term of Arithmetic Progression
- Sum of Arithmetic Progression
- Arithmetic Progression Formula (AP Formulas)