ARITHMETIC PROGRESSION

ARITHMETIC PROGRESSION

Formula

ARITHMETIC PROGRESSION (AP) Formula PDF Definition with Example

ARITHMETIC PROGRESSION –

  1. ARITHMETIC PROGRESSION (AP):

AP is sequence whose terms increase or decrease by a fixed number. this fixed number is called the common difference. if ‘a’ is the first term &‘d’ is the common difference, then ARITHMETIC PROGRESSION can be written as

(a)  nth term of this AP where

(b)  The sun of the first n terms: where is the last term.

(c)   Also nth term

Note:

(i)      Sum of first n terms of an A.P. is of the form An2 + Bn i.e. a quadratic expression in n, in such  case the common difference is twice the coefficient of n2. i.e. 2A

(ii)   nth term of an A.P. is of the form An + B i.e. a linear expression in n, in such case the coefficient of n is the common difference of the A.P. i.e. A

(iii)    Three numbers in AP can be taken as a – d, a, a + d ; four numbers in AP can be taken as a – 3d, a – d,

a + d, a + 3d five numbers in AP are a – 2d, a – d, a, a + 2d & six terms in ap are a – 5d, a – 3d, a – d,

a + 3d,  a + 5d etc.

(iv)    If for A.P. pth term is q, qth term is p, then rth term is

 

 

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