Arithmetic Progression

A set of numbers where the numbers are arranged in a definite order is called a sequence.

E.g. 1, 2, 3, 4 …………

In a sequence if difference is constant then the sequence is called an arithmetic progression.

In an A.P. the difference between two consecutive terms is constant and is denoted by d.

Difference d can be positive, negative or zero.

In an A.P. if the first term is a, and common difference is d then the terms in the sequence are a, (a+d), (a+2d), …….

nth term of an A.P.

tn =a+(n-1)d

using the above formula we can find the 100th term of the A.P. 5, 8, 11, 14, . . .

Here a=5 d=3

tn = a+(n-1)d

t 100 = 5 + (100-1)* 3

=5+ 99* 3

=5+ 297

t100 = 302

100th term of this A.P is 302.

Sum of first n terms of an A.P.

For the given Arithmetic Progression, if first term is a and common difference is d then

Sn= (n/2)*[2a+(n – 1)d]

Q. First term and common difference of an A.P. are 6 and 3 respectively; find S27 ?

Solution: a=6, d=3, S27=?

Sn= (n/2)*[2a + (n – 1)d]

S27= (27/2)*[12 + (27 – 1)3]

=(27/2)*90

=27 * 45

=1215

Therefore sum of 27 terms of given A.P. is 1215.

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