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if the sum of m terms of an ap to the sum of n terms of another ap is m2 to n2 (ratio),show that mth term to nth term is 2m-1 to 2n-1...

if the sum of m terms of an ap to the sum of n terms of another ap is m2 to n2 (ratio),show that  mth term to nth term  is 2m-1 to 2n-1...

Grade:11

1 Answers

Nehal Wani
21 Points
13 years ago

The APs have to be the same because their first terms and common difference can't get cancelled out then. Refer NCERT Ex9.2 Q12

 

Let a and b be the first term and the common difference of the A.P. respectively.

According to the given condition,

Putting m = 2m – 1 and n = 2n – 1 in (1), we obtain

From (2) and (3), we obtain

Thus, the given result is proved.

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