Saturday, December 15, 2018

Arithmetic Progressions

Arithmetic Progressions



(i) 1, 2, 3, 4 ...
(ii) - 5, - 1, 3, 7 ...
(iii) 1/3, 5/3, 9/3, 13/3 ....
(iv) 0.6, 1.7, 2.8, 3.9 ...
An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant

The common difference of the AP is a sequence is always fixed. It can be positive, negative or zero.

Let us denote the first term of an AP by a1, second term by a2, . . ., nth term by anand the common difference by d.

If the AP series has last term then it s finite Arithmetic Progression and if the AP series has infinite then it is called the Inifinite Arithmetic Progression

General form of AP is
a, a+d, a+2d, a+3d, a+4d, .... 

nth term an of the AP with first term a and common difference d is given by 
an = a + (n – 1) d
an is also called the general term of the AP.

Sum of n term of Arithmetic progression
Sn = (n/2)[2a + (n - 1)d]

If l is the last term of the finite AP, say the nth term, then the sum of all terms of the AP is given
S = (n/2)[a + l]

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