ARITHMETIC PROGRESSION (AP) Formula PDF Definition with Example
ARITHMETIC PROGRESSION –
- 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
(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