CBSE Class 10 Maths (Standard) 2017 · Paper 30/1/1 · Question 23

Arithmetic Progressions 4 marks Medium

The ratio of the sums of first

m

and first

n

terms of an A. P. is

m^{2} : n^{2}

. Show that the ratio of its

m^{t h}

and

n^{t h}

terms is

(2 m - 1) : (2 n - 1)

Answer

Since the sum condition forces

d = 2 a

, the

m

th term is

a (2 m - 1)

and the

n

th term is

a (2 n - 1)

, so their ratio is

(2 m - 1) : (2 n - 1)

, as required.

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