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# Sum of n Terms in Arithmetic Progression

TopA sequence of number in which difference between two successive number is a constant is known as Arithmetic Progression. In mathematics, arithmetic progression is representation as a, a + d, a + 2d, a + 3d, a + 4d …...... a + (n – 1) d, here value of 'a' represents initial value and 'd' represents common difference. For example: 8, 10, 12, 14, 16, 18 here initial value of A.P is 8 and difference between two Numbers is 2. Now we will see how to find the sum of n terms in arithmetic progression. Formula to find sum of n term in arithmetic progression is given by:
sum of n terms = n / 2 (2a + (n – 1) d).
It is more clear with help of example:
Like we have to find sum of first 22 terms of arithmetic progression: 8, 3, -2..........and so on, then we can calculate sum as shown below:
As we know that the sum of 'n' terms is given by:
sum of n terms = n / 2 (2a + (n – 1) d).
Here 'a' is initial value and the value of a = 8, 'd' is common difference, value of d = 3 – 8 = -5, and value of 'n' = 22. So put these value in formula, we get:
sum of n terms = n / 2 (2a + (n – 1) d).
sum of n terms = 22 / 2 (2 * 8 + (22 – 1) (-5)),
sum of n terms = 11 (16 + (21) (-5)),
sum of n terms = 11 [16 – 105],
sum of n terms = 11 [-89],
sum of n terms = -979,
So sum of first 22 terms is -979. This is all about Arithmetic progressions.