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If ‘S’ is the sum of a finite A.P. whose...

If ‘S’ is the sum of a finite A.P. whose first term is ‘a’ and last term is ‘l’, show that its common difference is equal to `(l^2-a^2)/(2S-a-l)`.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. In an A.P., if p^(th) term is 1/q and q^(th) term is 1/p, prove that t...

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  2. If the sum of first p terms of an A.P. is equal to the sum of the firs...

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  3. If ‘S’ is the sum of a finite A.P. whose first term is ‘a’ and last te...

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  4. In an A.P., of which a is the first term, if the sum of the first p te...

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  5. The sum of n terms of two arithmetic series are in the ratio of (7n + ...

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  6. The sum of n terms of arithmetic progressions are in the ratio (3n+ 8)...

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  7. The ratio of the sums of m and n terms of an A.P. is m^2: n^2. Show th...

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  8. A man saves ₹3200 during the first year, ₹ 3600 in the next year, ₹ 40...

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  9. A gentleman buys every year Bank’s certificates of value exceeding th...

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  10. A gentleman buys every year Bank’s certificates of value exceeding th...

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  11. If in an A.P. S1=6 and S7=105, prove that : S(n),S(n-3)::(n+3),(n-3)...

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  12. In an A.P., S(3)=6 and S(6)=3 prove that: 2(2n+1)S(n+4)=(n+4)S(2n+1)...

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  13. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respective...

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  14. If ‘a’ and ‘b’ are respectively the pth and qth terms of an A.P., show...

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  15. Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove...

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  16. Find the A.M. between : 3.7 and 5.5.

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  17. Find the A.M. between : 6 and -8.

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  18. Insert 3 arithmetic means between : 3 and 15.

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  19. Insert 3 arithmetic means between : 5 and 21.

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  20. Insert 5 arithmetic means between 8 and 26.

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