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An A.P is a sequence of numbers or terms in which each term except the first one is obtained by adding a fixed number or constant to the term preceding term.

The first term is denoted with â€˜aâ€™ and the fixed number is called the common difference denoted by â€˜dâ€™.

The common difference is the difference between two successive terms that is t_{2} â€“ t_{1} = t_{3} â€“ t_{2} = t_{4} â€“ t_{3} =â€¦.

**Sum of n terms** **of an AP**

The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by

S_{n} = $\frac{\text{n}}{\text{2}}$[ 2a + ( n - 1) d] or $\frac{\text{n}}{\text{2}}$[ a + l ] or $\frac{\text{n}}{\text{2}}$[ First term + Last term]. where l = a + (n - 1) d is called the last term.

If S_{n} be the sum of first n terms of sequence and t_{n} be the n^{th} term of sequence can be written as,

n^{th} term (t_{n}) = S_{n} - S_{n-1} and common difference(d) = a_{n} - a_{n-1} = S_{n} - 2S_{n-1} + S_{n-2} .

An A.P is a sequence of numbers or terms in which each term except the first one is obtained by adding a fixed number or constant to the term preceding term.

The first term is denoted with â€˜aâ€™ and the fixed number is called the common difference denoted by â€˜dâ€™.

The common difference is the difference between two successive terms that is t_{2} â€“ t_{1} = t_{3} â€“ t_{2} = t_{4} â€“ t_{3} =â€¦.

**Sum of n terms** **of an AP**

The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by

S_{n} = $\frac{\text{n}}{\text{2}}$[ 2a + ( n - 1) d] or $\frac{\text{n}}{\text{2}}$[ a + l ] or $\frac{\text{n}}{\text{2}}$[ First term + Last term]. where l = a + (n - 1) d is called the last term.

If S_{n} be the sum of first n terms of sequence and t_{n} be the n^{th} term of sequence can be written as,

n^{th} term (t_{n}) = S_{n} - S_{n-1} and common difference(d) = a_{n} - a_{n-1} = S_{n} - 2S_{n-1} + S_{n-2} .