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(a) The sum of 'n' terms of a progressio...

(a) The sum of 'n' terms of a progression is n(n + 1). Prove that it is an A..P. Also find its 10th term. (b) The sum of 'n' terms of a progression is `(3n^(2) - 5n).` Prove that it is an A.P. (c) If the sum of n terms of a series is `(5n^(2) + 3n)` then find its first five terms.

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The correct Answer is:
(a) 20 (c) 8,18,28,38,48
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NAGEEN PRAKASHAN ENGLISH-SEQUENCE AND SERIES-Exercise 9C
  1. (a) Find the value of x if 1 + 6 + 11 + ... + x = 189. (b) Find the ...

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  2. (a) How many terms of the A.P. 6 + 10 + 14 + ... has the sum 880 ? (b)...

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  3. (a) The sum of 'n' terms of a progression is n(n + 1). Prove that it i...

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  4. The sum of 5 and 15 terms of an A.P. are equal. Find the sum of 20 ter...

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  5. The sum of 20 and 28 terms of an A.P. are equal. Find the sum of 48 te...

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  6. In an A,P if the pth term is (1)/(q) and q^(th) terms is (1)/(p). Prov...

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  7. The sum of15 terms of an A.P. is zero and its 4th term is 12. Find its...

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  8. The common difference, last term and sum of terms of an A.P. are 4, 31...

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  9. If (0,-3)a n d(0,3) are the two vertices of an equilateral triangle, f...

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  10. If there are (2n+1) terms in A.P. , then prove that the ratio of the s...

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  11. In an A.P., if T(1) +T(5)+ T(10) +T(15)+ T(20) + T(24) = 225, find the...

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  12. The nth term of an A.P. is (5n-1). Find the sum of its 'n' terms.

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  13. The sum of 8 terms of an A.P. is 64 and sum of 17 terms is 289. Find t...

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  14. The ratio of sums ofn terms of two A.P'.s is (2n + 1) : (2n - 1). Prov...

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  15. The ratio of sums of n terms of two A.P'. is (7n + 1) : (4n + 27). Fin...

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  16. If the ratio of the sum of m terms and n terms of an A.P. be m^2 : n^2...

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  17. How many terms of the progression 54 + 51 + 48 +... has the sum 513 ? ...

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  18. The pth and qth terms of an A.P. are x and y respectively. Prove that ...

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  19. Show that the sum of an A.P. whose first term is a, the second term is...

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  20. If the first term of an A.P. is 100 and sum of its first 6 terms is 5 ...

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