CBSE Class 10 Maths (Standard) 2024 · Paper 30/2/1 · Question 26(a)

Arithmetic Progressions 3 marks Medium

If the sum of first

m

terms of an A.P. is same as sum of its first

n

terms

(m \neq = n)

, then show that the sum of its first

(m + n)

terms is zero.

Answer

From

S_{m} = S_{n}

and

m \neq = n

we get

2 a + (m + n - 1) d = 0

, so

S_{m + n} = \frac{m + n}{2} [2 a + (m + n - 1) d] = \frac{m + n}{2} \times 0 = 0

. Hence proved.

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