Question

The ratio of the sums of mand n terms of an A.P. is m²:n . Show that the ratioof the man and n'h terms is (2m -1): (2n-1).​

Answer 1

Answer:

Let Sm and Sn be the sum of first m and n terms of the AP whose first term and common difference of an ap is a and d respectively.then

Step-by-step explanation:

Sm/Sn=m/2{2a+(m-1)d}/n/{2(n-1)d

=m^2/n^2

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

2an+(mn-n)d=2am+(mn-m)d

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

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

2a=d

am/an=a+(m-1)d/a+(n-1)d

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

=a+2am-2a/a+2an-2a

2am-a/2an-a=2m-1/2n-1

Hence, ratio of mth and nth term is 2m-1:2n-1...

Answer 2

Answer:

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