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If `S_n` denotes the sum of the first `n` terms of an A.P., prove that `S_(30)=3(S_(20)-S_(10))` .

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RD SHARMA-ARITHMETIC PROGRESSIONS-All Questions
  1. The sum of the first n terms of an A.P. is 3n^2+6n . Find the n ...

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  2. The sum of the first 7 terms of an AP is 63 and the sum of its next 7 ...

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  3. If Sn denotes the sum of the first n terms of an A.P., prove tha...

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  4. The sum of first n terms of an A.P. is 5n-n^2 . Find the n t h t...

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  5. The sum of the first n terms of an A.P. is 4n^2+2n . Find the n ...

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  6. If the 10 t h term of an A.P. is 21 and the sum of its first ten te...

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  7. The first and the last terms of an AP are 7 and 49 respectively. If...

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  8. If Sn denotes the sum of first n terms of an A.P., prove that S(...

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  9. If the sum of the first n terms of an A.P. is 1/2(3n^2+7n), then find ...

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  10. The sum of first 9 terms of an A.P. is 162. The ratio of its 6th t...

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  11. Define an arithmetic progression.

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  12. Write the common difference of an A.P. whose n t h term is an=3n+7 ...

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  13. Which term of the sequence 114 ,\ 109 ,\ 104 ,\ is the first ne...

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  14. Write the value of a(30)-a(10) for the A.P. 4,\ 9,\ 14 ,\ 19 ,\ ...

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  15. Write 5t h term from the end of the A.P. 3,\ 5,\ 7,\ 9,\ ddot,\ 201...

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  16. Write the value of x for which 2x ,\ x+10 and 3x+2 are in A.P.

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  17. Write the n t h term of an A.P. the sum of whose n terms is Sn .

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

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

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  20. If the sum of n terms of an A.P. is Sn=3n^2+5n . Write its co...

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