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SAI International School

Class X

Mathematics – Lesson Notes
Chapter-5: Arithmetic Progression

Sub topics: Sum of ‘n’ terms

Prove that the sum S n of n terms of an Arithmetic Progress (A.P.) whose first term ‘a’
and common difference ‘d’ is

S = [2a + (n - 1)d]

Or, S = [a + l], where l = last term = a + (n - 1)d

Proof:

Suppose, a 1, a 2, a 3, ………..a n be an Arithmetic Progression whose first term is a and
common difference is d.

Then,

a 1 = a

a 2 = a + d

a 3 = a + 2d

a 4 = a + 3d

………..

………..

a n = a + (n - 1)d

Now,

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