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(i) Show that the sum of n consecutive o...

(i) Show that the sum of n consecutive odd integers beginning with 1 equals `n^(2)`.
(ii) show that the sum of first n even numbers is equal to `(1+1/n)` times the sum of first n odd numbers.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE 9 (c) LATQ
  1. (i) If the sum of a certain number of terms of the A.P. 25,22,19,……………...

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  2. If the first term of an A.P. is 2 and the sum of the first five terms ...

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  3. If 12th term of an A.P. is -13 and the sum of the first four terms ...

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  4. (i) Show that the sum of n consecutive odd integers beginning with 1 e...

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  5. (i) Find the sum of odd integers from 1to 2001. (ii) Find the sum of...

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  6. How many terms are there in the A.P. whose first and fifth terms are ...

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  7. Prove that a sequence in an A.P., if the sum of its n terms is of the ...

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

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  9. If the first term a(1) of an A.P. is 22, the common difference d=-4 an...

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

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  11. The first and last terms of an AP are a and l respectively. If S be th...

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  12. In an A.P. of which a is the first term if the sum of the first p term...

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  13. (i) The sum of n terms of two arithmetic series are in the ratio of (7...

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  14. A man saves Rs. 3200 during the first year, Rs. 3600 in the next year ...

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  15. A gentleman buys every year Bank's certificates of value exceeding the...

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  16. a. If in an A.P. S(1)=6 and S(7)=105 prove that : S(n),S(n-3)::(n+3)...

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  17. if the pth term of an A.P. is x and qth term is y, show tht the sum of...

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