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If S(n) denotes the sum of first n terms...

If `S_(n)` denotes the sum of first `n` terms of an AP, then prove that `S_(12)=3(S_(8)-S_(4)).`

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The correct Answer is:
`= 3 [S_(8) - S_(4)]`
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EDUCART PUBLICATION-ARITHMETIC PROGRESSIONS-SHORT ANSWER (SA - II) TYPE QUESTIONS
  1. Show that the sum of an A.P. whose first term is a, the second term is...

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  2. The first term of an AP is -5 and the last term is 45. If the sum of t...

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  3. If S(n) denotes the sum of first n terms of an AP, then prove that S(1...

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  4. If sum of first 6 terms of an AP is 36 and that of the first 16 terms ...

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  5. The sum of the first n terms of an AP whose first term is 8 and the co...

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  6. If the m^(th) term of an A.P. is 1/n and the n^(th) term is 1/m, show ...

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  7. find the sum of n terms of the series (4-1/n)+(4-2/n)+(4-3/n)+...........

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  8. For what value of n, the nth terms of the arithmetic progressions 63, ...

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  9. Find the sum of the first 40 positive integers divisible by 6.

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  10. Divide 56 in four parts in A.P. such that the ratio of the product of ...

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  11. If the sum of first 7 terms of an A.P. is 49 and that of its 17 terms ...

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  12. If the sum of first m terms of an A.P. is the same as the sum of its f...

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  13. How many terms of the A.P. 9, 17, 25, …..must be taken to give a sum o...

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  14. The houses of a row are numbered from 1 to 49. Show that there is a va...

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  15. The 14th term of an A.P. is twice its 8th term. If its 6th term is -8,...

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  16. The digits of a positive integer, having three digits, are in A.P. and...

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  17. Find the sum of first 24 terms of the list of numbers whose nth term ...

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  18. Determine the AP whose third term is 16 and the 7th term exceeds the 5...

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  19. Justify whether it is true to say that the following are the nth terms...

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  20. Justify whether it is true to say that the following are the nth terms...

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