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**

**Definition of Arithmetic Progression****General Form of an Arithmetic Progress****Arithmetic Mean****Sum of the First n Terms of an Arithmetic Progression****Sum of the Cubes of First n Natural Numbers****Sum of First n Natural Numbers****Sum of the Squares of First n Natural Numbers****Properties of Arithmetic Progression****Selection of Terms in an Arithmetic Progression****Arithmetic Progression Formulae****Problems on Arithmetic Progression****Problems on Sum of 'n' Terms of 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.