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If the sum of the first n terms of a seq...

If the sum of the first n terms of a sequence is of the form `An^2+ Bn`, where A, B are constants independent of n, show that the sequence is an A.P. Is the converse true ? Justify your answer.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
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  2. How many terms are there in A.P. whose first and fifth terms are -14 a...

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  3. If the sum of the first n terms of a sequence is of the form An^2+ Bn,...

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  4. If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what ...

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  5. If the first term a1 of an A.P. is 22, the common difference d = -4 an...

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

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

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

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

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

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

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

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

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  16. 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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  17. 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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  18. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respective...

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

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

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