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If S(1), S(2), S(3) be the sums of n ter...

If `S_(1), S_(2), S_(3)` be the sums of n terms of three aA.P.'s, the first term of each A.P. being 1 and the respective common differences are 1, 2, 3 then show that, `S_(1) + S_(3) = 2S_(2)`.

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Long Answer Type Questions)
  1. The sum of the first p terms of an A.P. is q and the sum of the first ...

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  2. If the pth and qth terms of an A.P. be a and b respectively, show that...

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  3. If S(1), S(2), S(3) be the sums of n terms of three aA.P.'s, the first...

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  4. If the sums of n, 2n and 3n terms of an A.P. be S(1), S(2), S(3) respe...

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  5. The sums of n terms of two A.P.'s are in the ratio (4n-13) : (3n + 10)...

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  6. The sums of first n terms of two A.P.'s are in the ratio (3n+5) : (5n ...

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  7. Insert a number of arithmetic means between 4 and 34 such that the sum...

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  8. If a, b, c are in A.P. then show that, a((1)/(b)+(1)/(c )), b((1)/(c )...

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  9. Three positive numbers a, b, c are in A.P. Prove that (1)/(sqrt(b)+sqr...

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  10. If a(1), a(2), a(3),…, a(n) be in A.P. Show that, (1)/(a(1)a(2)) + (...

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  11. If a(1), a(2), a(3),…, a(2k) are in A.P., prove that a(1)^(2) - a(2)^(...

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

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  13. Find the sum to n terms of each of the following series : 2.4 + 6.8 ...

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  14. Find the sum to n terms of each of the following series : 1^(2) + 3^...

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  15. Find the sum to n terms of each of the following series : 1.3 .5 + 3...

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  16. Find the sum of the following series : 3.1^(2) + 4.2^(2) + 5.3^(2) +...

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  17. Find the sum of the following series : 1+3+6+10+15+… to n terms.

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  18. Find the sum of the following series : 1+5+12+22+35+…. to n terms.

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  19. The sum of first n terms of a series is n^(2) + an + b. Show that b = ...

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  20. If n is a positive integer, show that, (n+1)^(2) + (n+2)^(2) + …+ 4n...

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