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The nth term of an A.P. is p and the sum...

The nth term of an A.P. is p and the sum of its first n terms is q. Prove that its first term is `(1)/(n)(2q-p n)`.

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Short Answer Type Questions)
  1. How many terms of the series {27+24+21+…} must be added to get the sum...

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  2. The first and last terms of an A.P. having a finite number of terms ar...

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  3. The nth term of an A.P. is p and the sum of its first n terms is q. Pr...

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  4. Find the sum of the series {2+3+5+9+8+15+11+21+….} to {2n+1} terms.

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  5. How many even numbers are there between 91 and 259 ? Find also the sum...

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  6. Find the sum of all the multiples of 11 between 100 and 400.

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  7. Find the sum of all the numbers of the form n^(3) lying between 100 an...

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  8. The nth term of an A.P. is 7n-5, find the sum of first 20 terms of the...

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  9. The middle term of an arithmetic progression having (2n+1) terms is m,...

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  10. The sum of three integers in A.P. is 15 and their product is 80, find ...

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  11. The sum of four integers in A.P. is 20 and the sum of their squares is...

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  12. Divide 21 into three parts in A.P. such that the product of the first ...

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  13. The ratio of the 11th and 14th terms of an A.P. is 7:9, find the ratio...

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  14. Insert five arithmetic means between (-19) and 23.

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  15. There are n arithmetic means between 4 and 31 such that the second mea...

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  16. If a, b, c are In A.P., then show that, (a+2b-c) (2b+c-a)(c+a-b) = 4...

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  17. If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2...

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  18. If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a...

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  19. If the pth , qth and rth terms of an A.P. be P, Q and R respectively t...

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

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