__Sequence and Series__

__Arithmetic Progression (AP)__

- An arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a constant ‘d’ to the preceding term. The constant d is called the common difference.

- An arithmetic progression is given by a, (a + d), (a + 2d), (a + 3d), …

where a = the first term, d = the common difference

- If a, b, c are in AP then b = (a + c)/2
- n
^{th}term of an arithmetic progression

t_{n} = a + (n – 1)d

where t_{n} = n^{th} term, a= the first term, d= common difference

- Number of terms of an arithmetic progression

n=(*l*-a)/d+1

where n = number of terms, a= the first term , l = last term, d= common difference

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__FORMULAS__

__ADDITIONAL NOTES ON AP__

To solve most of the problems related to AP, the terms can be conveniently taken as

3 terms: (a – d), a, (a +d)

4 terms: (a – 3d), (a – d), (a + d), (a +3d)

5 terms: (a – 2d), (a – d), a, (a + d), (a +2d)

__Harmonic Progression(HP)__

__Geometric Progression (GP)__

Geometric Progression (GP) is a sequence of non-zero numbers in which the ratio of any term and its preceding term is always constant.