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Prove that a sequence in an A.P., if the...

Prove that a sequence in an A.P., if the sum of its `n` terms is of the form `A n^2+B n ,w h e r eA ,B` are constants.
(a) an AP
(b) a GP
(c) a HP
(d) None of these

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. The ratio of the sum of m and n terms of an A.P. is m^2: n^2dot Show t...

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  2. The interior angles of a polygon are in A.P. the smallest angle is 120...

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  3. Prove that a sequence in an A.P., if the sum of its n terms is of the...

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  4. If the first term of an A.P. is 2 and the sum of first five terms is ...

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  5. The sum of n terms of two arithmetic progressions are in the ratio (3n...

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  6. Let Sk be the sum of first k terms of an A.P. What must this progressi...

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  7. Find the sum of the following arithmetic progression: 50,46,42,… upto ...

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  8. Find the sum of the following series : (i) 1,3,5,7...upto 12 terms.

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  9. Find the sum of the following arithmetic progression: 3,9/2,6,15/2,…...

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  10. Find the sum of the following arithmetic progression: 41,36,31,…….to 1...

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  11. Find the sum of the following arithmetic progression: a+b ,\ a-b ,\...

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  12. Find the sum of the following arithmetic progression: (x-y)/(x+y),(3x-...

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  13. Find the sum of the following series: 2+5+8+. . . .+182

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  14. Find the sum of the following series: 101+99+97+....+47

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  15. Find the sum of the following series: (a-b)^2+(a^2+b^2)+(a+b)^2+...+[(...

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  16. Find the sum of first n natural numbers.

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  17. Find the sum of all natural numbers between 1 and 100, which are divis...

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  18. Find the sum of the first n odd numbers

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  19. Find the sum of all odd numbers between 100 and 200.

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  20. Show that the sum of all odd integers between 1 and 1000 which are div...

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