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If the ratio of the sum of m terms and n terms of an A.P. be `m^2 : n^2`, prove that the ratio of its mth and nth terms is `(2m-1): (2n-1)`.

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If the ratio of the sum of first n terms of two AP's is (7n+1) : (4n + 27), then find the ratio of their mth terms.

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ICSE-SEQUENCE AND SERIES -EXERCISE 14 (c)
  1. The interior angles of a polygon are in arithmetic progression. The sm...

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  2. Determine the sum of first 35 terms of an A.P. if t(2), = 1 and t(7) ,...

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  3. Find the sum of all natural numbers between 100 and 1000 which are mul...

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  4. How many terms of the A.P. 1,4,7.... are needed to give the sum 715?

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  5. Find the rth term of an A.P., sum of whose first n terms is 2n + 3n^(2...

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  6. In an arithmetical progression, the sum of p terms is m and the sum of...

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  7. The sum of the first fifteen terms of an arithmetical progression is 1...

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  8. The sum of the first six terms of an arithmetic progression is 42. The...

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  9. A sum of रु6240 is paid off in 30 instalments, such that each instalme...

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  10. The nth term of an A.P. is p and the sum of the first n term is s. Pro...

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  11. The sum of the first n terms of the arithmetical progression 3, 5(1)/(...

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  12. If the sum of the first 4 terms of an arithmetic progression is p, the...

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  13. The last term of an A.P. 2, 5, 8, 11, .... is .x. The sum of the terms...

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  14. A gentleman buys every year Banks' certificates of value exceeding the...

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  15. If the sums of the first n terms of two A.P.'s are in the ratio 7n-5: ...

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  16. If the ratio of the sum of m terms and n terms of an A.P. be m^2 : n^2...

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  17. Let a(1) , a(2) , a(3) , ..... be terms of an A.P. If (a(1)+a(2)+........

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  18. If the sum of n, 2n, 3n terms of an A.P are S(1), S(2), S(3), respecti...

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  19. If the sum of p terms of an A.P. is q and the sum of q terms is p, sho...

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  20. The ratio between the sum of n terms of two A.P.'s is (7n + 1) : (4n+2...

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