KVPY SA Exam 2018 Question Paper

Question : 3 of 80

Marks: +1, -0

Suppose the sum of the first m terms of arithmetic progression is n and the sum of its first n terms is m, where m ≠ n. Then the sum of the first ( m + n) terms of the arithmetic progression is

1 – mn
mn – 5
–(m + n)
m + n

Validate

Solution:

S_m =m/2[2a + (m -1)d] = n

….(1)

S_n =n/2 [2a + (n -1)d] = m

….(2)
By (1) and (2)

(m -n)a + (m -n) \{m + n -1\} d /2

= -(m -n)

⇒

2a + (m + n -1)d = -2 (m ≠ n)

⇒

S_{m+n }={m +n}/2[2a + (m + n -1)d]

= -(m + n)

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