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Prove that the product of the 2^ (nd) a...

Prove that the product of the `2^ (nd) ` and `3 rd` terms of an A.P.'exceeds the product of the `1st` and `4^ (th) ` by twice the square of the difference between the `1^ (st) `, and `2^ (nd) `.

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V PUBLICATION-SEQUENCES AND SERIES-QUESTIONBANK
  1. If S1, S2, S3 are the sum of first n natural numbers, their squares an...

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

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  3. Show that (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. .+n...

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  4. A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and...

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  5. Shamshad Ali buys a scooter for Rs. 22000. He pays Rs. 4000 cash and a...

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  6. A person writes a letter to four of his friends. He asks each one of t...

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  7. A man deposited Rs. 10000 in a bank at the rate of 5 % simple interest...

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  8. A manufacturer reckons that the value of a machine, which costs him Rs...

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  9. 150 workers were engaged to finish a job in a certain number of days. ...

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  10. Write the first 'three terms of the sequences whose nth term Tn is giv...

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  11. Show that the sequence: log a, log ((a^2)/b), log(( a^3)/(b^2)) . . is...

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  12. Which term of the sequence 37,32,27,22,... is -103

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  13. Find the 20^( th) term of the series 2 xx 4+4 xx 6+6 xx 8+. . .,+ n t...

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  14. The 7^th term of an AP is 34 and the 15^thterm is 74. Find the 40^th t...

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  15. Prove that the product of the 2^ (nd) and 3 rd terms of an A.P.'excee...

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  16. Find the sum of all three digit numbers which leave the remainder 1 wh...

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  17. If the 'sum of first m terms of an A . P. be n and the sum of first n ...

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  18. Insert three A.M.s between 11 and 14

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  19. Find the n^ (th) and 9^ (th) terms of the sequence 3,6,12,24, . .

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  20. For what value of n, the n^ (th) terms of the series " 5+10+20+.........

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