Loading [MathJax]/jax/output/HTML-CSS/jax.js

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) = tn = a + (n - 1)d

(ii) The sum of the first n terms = Sn = n2(a + l) = Numberofterms2(First term + Last term)

or, Sn = n2[2a + (n - 1)d] where l = last term = nth term = a + (n - 1)d.


2. (i) The sum of first n natural numbers (Sn)= n2(n + 1)

i.e., 1 + 2 + 3 + 4 + 5 + .................... + n = n2(n + 1)

(ii) The sum of the squares of first n natural numbers (Sn)= 16n(n + 1)(2n + 1)

i.e., 12 + 22 + 32 + 42 + 52 + ................... + n2  = 16n(n + 1)(2n + 1)

(iii) The sum of the cubes of first n natural numbers (Sn) = {12n(n +1)}2

i.e., 13 + 23 + 33 + 43 + 53 + ........... + n3 = {12n(n +1)}2


3. The arithmetic mean between two given quantities a and b = ½ × (Sum of the given quantities) = a+b2.

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. Successor and Predecessor | Successor of a Whole Number | Predecessor

    Jul 29, 25 12:59 AM

    Successor and Predecessor
    The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number…

    Read More

  2. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 28, 25 01:52 PM

    Volume of a Cuboids
    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  3. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  4. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  5. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More