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.
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
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 * 45
Therefore sum of 27 terms of given A.P. is 1215.