The ratio of the sums of m and n terms of an A-P- is m2- n2- Show that the ratio of mth and nth term is 2 m-1-2 n-1-

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Standard XII

Mathematics

Sum of Infinite Terms

The ratio of ...

Question

The ratio of the sums of m and n terms of an A.P. is m²: n². Show that the ratio of m^thand n^th term is (2m – 1): (2n – 1).

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Solution

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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The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nth term is (2m – 1): (2n – 1).

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.

The ratio of the sums of m and n terms of an A.P. is m²: n². Show that the ratio of m^thand n^th term is (2m – 1): (2n – 1).

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.