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Let Sn be the sum of first n terms of ...

Let `S_n` be the sum of first `n` terms of an A.P. with non-zero common difference. Fine the ratio of first term and common difference if `(S_(n_1n_2))/(S_(n_1))` is independent of `n_1dot`

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. The p^(t h) term of an A.P. is a and q^(t h) term is b Prove that t...

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  2. If S1,S2, S3, Sm are the sums of n terms of m A.P. ' s whose first ter...

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  3. Let Sn be the sum of first n terms of an A.P. with non-zero common d...

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  4. If there are (2n+1) terms in A.P., then prove that the ratio of the su...

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  5. The ratio of the sum of n terms of two A.P. s is (7n+1):(4n+27) . Fin...

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  6. Show that x^2+x y+y^2,z^2+xz+x^2, y^2+y z+z^2, are consecutive terms o...

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  7. If a ,b ,c are in A.P., prove that: i.(a-c)^2=4(a-b)(b-c) ii.a^2+c^2...

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  8. Find the sum of all those integers between 100 and 800 each of which o...

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  9. If the sum of m terms of an A.P. is equal to the sum of either the nex...

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  10. Suppose x and y are two real numbers such that the rth mean between xa...

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  11. The sum of two numbers is (13)/6dot An even number of arithmetic means...

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  12. The digits of a positive integer, having three digits, are in A.P. and...

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  13. If x ,y ,z are in A.P. and A1 is the A.M. of xa n dya n dA2 is the A.M...

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  14. A man repays a loan of R s .3250 by paying R s .20 in the first month ...

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  15. If (b+c-a)/a ,(b+c-a)/b ,(b+c-a)/c , are in A.P., prove that 1/a ,1/b ...

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  16. If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a...

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  17. If a ,b ,c are in A.P., prove that 1/(b c),1/(c a),1/(a b), is al...

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  18. If a^2,b^2,c^2 are in A.P., then prove that the following are also in ...

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  19. Two cars start together in the same direction from the same place. The...

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  20. Find an A.P. in which the sum of any number of terms is always three ...

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