2. 3, 7, 11, 15 , ………
3. a , a+ d , a +2d, a+ 3d………….
The three examples shown above are the examples of the arithmetic progression: In the first series we can see that the difference between the two consecutive numbers is 1 that is (2-1 or 4-3 etc). Similarly in the second series 3, 7, 11, 15… the difference between two consecutive terms is 4 that is (7-3 or 11-7 etc).
The series a , a+ d , a +2d, a+ 3d…………. is called the general arithmetic progression which is used in daily life..
Here first term is “a”, the difference between two terms (a+ d-a) is ”d” and the last tem is denoted by L which is not mentioned in this series.
Let us discuss some Basic Formulas used for calculating the series .
The sum of the series can be calculates as:
SM = n/2(2a+ (n-1)d)
Where "n" is the number of terms. "a" is the first term and "d" is the difference between two consecutive terms .
The nth term of the series can be calculated with the help of the formulas:
tn = a+(n-1)d
Here tn is the nth term which has to be calculated, a is the first term , n is the number of terms and d is the difference between two terms.
Similarly the formula for the Sum of series when last term is also present in the series is:
Sl = n/2(a+l)
Where, ‘l’ is the last term of series.