Question

The ratio of the sums of mand n terms of an A.P. is m?: n. The ratio of mth and nth terms is :
(A) (m+ 1): (n+1)
(B) (2m +1):(2n + 1)
(C) (2m - 1): (2n-1)
(D)m:n.
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Answer 1

Sum of m terms of an A.P. = m/2 [2a + (m -1)d]

Sum of n terms of an A.P. = n/2 [2a + (n -1)d]

m/2 [2a + (m -1)d] / n/2 [2a + (n -1)d] = m2 : n2

⇒ [2a + md - d] / [2a + nd - d] = m/n

⇒ 2an + mnd - nd = 2am + mnd - md

2an - 2am = nd - md

2a (n -m) = d(n - m)

2a = d

Ratio of m th term to n th term:

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

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

(2m - 1) / (2n -1)

So, the ratio of m th term and the n th term of the arithmetic series is (2m - 1) : (2n -1) Ans....