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The sums of n terms of three arithmetica...

The sums of `n` terms of three arithmetical progressions are `S_1, S_2a n dS_3dot` The first term of each unityand the common differences are `1,2a n d3` respectively. Prove that `S_1+S_3=2S_2dot`

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NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Exercise 9C
  1. The sum of 5 and 15 terms of an A.P. are equal. Find the sum of 20 ter...

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

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  3. The pth and qth terms of an A.P. are(1)/(4)and(1)/(p) respectively. Pr...

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  4. The sum of 15 terms of A.P. is zero. Its 4th term is 12. Find its 14th...

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

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  6. The sum of m and n terms of an A.P. are n and m respectively. Prove t...

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

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

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  9. The sum of 8 terms of an A.P. is -64 and sum of 17 terms is 289. Find ...

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

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

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  12. The ratio of the sums of m terms and n terms of an A.P. is m^(2) : n^(...

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

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

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

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

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  17. The first term, last term and common difference of an A.P are respecti...

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  18. Write the sum of first n even natural numbers.

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  19. If Sn denotes the sum of n terms of an A.P. whose common difference is...

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  20. The sums of n terms of three arithmetical progressions are S1, S2a n d...

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