Arithmetic Progression Formulae

We will discuss about different types of Arithmetic Progression formulae.

1. Let ‘a’ be the first term and ‘d’ the common difference of an Arithmetic Progression. Then its

(i) General term (nth term) = t\(_{n}\) = a + (n - 1)d

(ii) The sum of the first n terms = S\(_{n}\) = \(\frac{n}{2}\)(a + l) = \(\frac{Number of terms}{2}\)(First term + Last term)

or, S\(_{n}\) = \(\frac{n}{2}\)[2a + (n - 1)d] where l = last term = nth term = a + (n - 1)d.


2. (i) The sum of first n natural numbers (S\(_{n}\))= \(\frac{n}{2}\)(n + 1)

i.e., 1 + 2 + 3 + 4 + 5 + .................... + n = \(\frac{n}{2}\)(n + 1)

(ii) The sum of the squares of first n natural numbers (S\(_{n}\))= \(\frac{1}{6}\)n(n + 1)(2n + 1)

i.e., 1\(^{2}\) + 2\(^{2}\) + 3\(^{2}\) + 4\(^{2}\) + 5\(^{2}\) + ................... + n\(^{2}\)  = \(\frac{1}{6}\)n(n + 1)(2n + 1)

(iii) The sum of the cubes of first n natural numbers (S\(_{n}\)) = {\(\frac{1}{2}\)n(n +1)}\(^{2}\)

i.e., 1\(^{3}\) + 2\(^{3}\) + 3\(^{3}\) + 4\(^{3}\) + 5\(^{3}\) + ........... + n\(^{3}\) = {\(\frac{1}{2}\)n(n +1)}\(^{2}\)


3. The arithmetic mean between two given quantities a and b = ½ × (Sum of the given quantities) = \(\frac{a + b}{2}\).

4. (i) If the sum of three terms in Arithmetic Progression be given, assume the numbers as a - d, a and a + d. Here common difference is d.

(ii) If the sum of four terms in Arithmetic Progression be given, assume the numbers as a - 3d, a - d, a + d and a + 3d.

(iii) If the sum of five terms in Arithmetic Progression be given, assume the numbers as a - 2d, a - d, a, a + d and a + 2d. Here common difference is 2d.

(iv) If the sum of six terms in Arithmetic Progression be given, assume the numbers as a - 5d, a - 3d, a - d, a + d, a + 3d and a + 5d. Here common difference is 2d.

Arithmetic Progression




11 and 12 Grade Math 

From Arithmetic Progression Formulae to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Multiplication Table | Learn Tables from 0 – 25 | Multiplication Table

    Jan 14, 25 11:53 PM

    multiplication table
    In math multiplication table we will learn the tables from 0 – 25. These multiplication tables help the students to learn the essential multiplication facts. Multiplication tables are very important f…

    Read More

  2. 3rd Grade Math Worksheets |3rd Grade Math Sheets|3rd Grade Math Lesson

    Jan 14, 25 11:02 PM

    3rd Grade Math Worksheets
    3rd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. Teachers and parents can also follow the worksheets to guide the students.

    Read More

  3. 3rd Grade Subtraction Worksheet | 3-Digit Subtraction Worksheets | Ans

    Jan 14, 25 01:57 PM

    Fill in the Missing Numbers Subtraction and Addition
    In 3th Grade Addition Worksheet we will solve how to subtract 3-digit numbers by expansion, subtraction of 3-digit numbers without regrouping, subtraction of 3-digit numbers with regrouping, propertie…

    Read More

  4. Facts about Subtraction | Subtraction of Small Numbers|Solved Examples

    Jan 14, 25 12:29 AM

    The operation to finding the difference between two numbers is called subtraction. Let us know some facts about subtraction which will help us to learn subtraction of large numbers. 1. Subtraction wit…

    Read More

  5. Word Problems on Subtraction |Worksheet on Subtraction Word Problems |

    Jan 14, 25 12:21 AM

    Subtraction Problem
    In word problems on subtraction we need to read the question carefully and understand what we need to find out. We know, in subtraction the larger number from which we subtract the other number (the s…

    Read More