What is the arithmetic sum formula?

The arithmetic sum formula is Sn = n/2 {2a + (n-1) d} where Sn is the sum of n-terms of an arithmetic progression, the first term is ‘a’ and the common difference between any two consecutive terms is given by d.

In mathematics, such a series of numbers is called an arithmetic progression. There are two types of progressions or series. The other progression is called a geometric progression.

For instance, the series of numbers 5, 10, 15, 20, 25 and 30 form an arithmetic progression. Here, the first term is five and the common difference is also five. The sum of the first six terms can be obtained as follows.

Sn = n/2 {2a + (n-1) d}

= 6/2 x {2x5+ (6-1) (5)}

= 3 x {10 + (6-1) (5)}

= 3 x 35

= 105