**Category : **JEE Main & Advanced

A sequence of numbers \[<{{t}_{n}}>\] is said to be in arithmetic progression (A.P.) when the difference \[{{t}_{n}}-{{t}_{n-1}}\] is a constant for all *n* Î *N*. This constant is called the common difference of the A.P. and is usually denoted by the letter *d*.

If \['a'\] is the first term and \['d'\] the common difference, then an A.P. can be represented as \[a,\,a+d,a+2d,\,a+3d,........\]

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*Example*** :** 2, 7, 12, 17, 22, …… is an A.P. whose first term is 2 and common difference 5.

Algorithm to determine whether a sequence is an A.P. or not.

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**Step I: **Obtain \[{{a}_{n}}\] (the \[{{n}^{th}}\] term of the sequence).

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**Step II: **Replace \[n\] by \[n-1\] in \[{{a}_{n}}\] to get \[{{a}_{n-1}}\].

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**Step III: **Calculate \[{{a}_{n}}-{{a}_{n-1}}\].

If \[{{a}_{n}}-{{a}_{n-1}}\] is independent from \[n,\] the given sequence is an A.P. otherwise it is not an A.P.

\[\therefore \] \[{{t}_{n}}=An+B\] represents the \[{{n}^{th}}\] term of an A.P. with common difference *A*.

*play_arrow*Definition*play_arrow*General Term of an A.P.*play_arrow*Selection of Terms in an A.P.*play_arrow*Sum of n terms of an A.P.*play_arrow*Arithmetic Mean*play_arrow*Properties of A.P.

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