An arithmetic progression is list of numbers in which the difference between any two consecutive terms is constant.
e.g 4,710,13,…… is A. P with a=4 and d=3
Each member of the sequence is called term.
General Term of A.P. THEOREM Let ‘a ’ be the first term and ‘d ’ be the common difference
Since each term of an A.P. is obtained by adding common difference to the preceding term. Therefore,
Similarly, we have
Observing the pattern in equation (1), 2), (3) and (4), we find that
Let there be an A.P. with first term ‘a ’ and common difference ‘d ’. If there are ‘m ’ terms in
Also, if I is the last term of the A.P., then term from the end is the nth term of an A.P. whose first term is I and common difference is –d.
MIDDLE TERM(S) OF A FINITE A.P.
Let there be a finite A.P. with ‘ ’n terms whose first term is ‘a ’ and common difference is ‘d’.
If n is odd, then
term is the middle term and is given by
If n is even, then
are middle term given by
Sum of n terms of AP:
Sum of first n terms of A.P. is given by
THEOREM The sum of n terms of an A.P. with first term ‘ a’ and common difference ‘ d’ is
Writing the above series in a reverse order, we get
Adding the corresponding terms of equations (1) and (2), we get
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