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In an A,P if the pth term is (1)/(q) and...

In an A,P if the pth term is `(1)/(q) and q^(th)` terms is `(1)/(p)`. Prove that the sum of first pq term is `(1)/(2)` (pq+1) where, `(p!=q)`

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NAGEEN PRAKASHAN ENGLISH-SEQUENCE AND SERIES-Exercise 9C
  1. The sum of 5 and 15 terms of an A.P. are equal. Find the sum of 20 ter...

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  2. The sum of 20 and 28 terms of an A.P. are equal. Find the sum of 48 te...

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  3. In an A,P if the pth term is (1)/(q) and q^(th) terms is (1)/(p). Prov...

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  4. The sum of15 terms of an A.P. is zero and its 4th term is 12. Find its...

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  5. The common difference, last term and sum of terms of an A.P. are 4, 31...

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  6. If (0,-3)a n d(0,3) are the two vertices of an equilateral triangle, f...

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

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  8. In an A.P., if T(1) +T(5)+ T(10) +T(15)+ T(20) + T(24) = 225, find the...

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  9. The nth term of an A.P. is (5n-1). Find the sum of its 'n' terms.

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  10. The sum of 8 terms of an A.P. is 64 and sum of 17 terms is 289. Find t...

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  11. The ratio of sums ofn terms of two A.P'.s is (2n + 1) : (2n - 1). Prov...

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  12. The ratio of sums of n terms of two A.P'. is (7n + 1) : (4n + 27). Fin...

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  13. 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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  14. How many terms of the progression 54 + 51 + 48 +... has the sum 513 ? ...

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  15. The pth and qth terms of an A.P. are x and y respectively. Prove that ...

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  16. Show that the sum of an A.P. whose first term is a, the second term is...

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  17. If the first term of an A.P. is 100 and sum of its first 6 terms is 5 ...

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  18. The first term, last term and common difference of an A.P are respecti...

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  19. Write the sum of first n even natural numbers.

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  20. If S(n) denotes the sum of n terms of an A.P. with common difference d...

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