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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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NAGEEN PRAKASHAN-ARITHMETIC PROGRESSION-Exercise 5c
  1. How many terms of the A.P. 54, 51, 48, ... has the sum 513 ? Explain t...

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  2. Find the value of 'x' if (i) 1+6+11+...+x=189 (ii) 1+1+4+7+10+...+...

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  3. (i) Find the sum of first 200 even natural numbers. (ii) Find the su...

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  4. Find the sum of n terms of an A.P. whose nth term is (2n+1).

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  5. The sum of n terms of a series is n(n+1) . Prove that it is an A.P. al...

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  6. The sum of n terms of a series is (3n^(2)+2n). Prove that it is an A.P...

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  7. The sum of first 5 terms and first 15 terms of an A.P. are equal. Fin...

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  8. The sum of first 8 terms and first 24 terms of an A.P. are equal. Find...

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

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  10. The sum of first 8 terms of an A.P. is 64 and that of first 15 terms i...

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  11. Find the sum of first 24 terms of the A.P. a1, a2, a3, , if it is kno...

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  12. The first term, last term and common difference of an A.P. are respect...

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

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  14. Yasmeen saves Rs. 32 during the first month, Rs. 36 in the second mont...

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  15. The sum of the first five terms of an A.P. and the sum of the first s...

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  16. 200 logs are stacked in such a way that there are 20 logs in the botto...

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  17. The ratio of the sum of n terms of two A.P. s is (7n+1):(4n+27) . Fin...

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

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  19. The famous mathematician associated with finding the sum of the first ...

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  20. If S1 is the sum of an AP of 'n' odd number of terms and S2 be the sum...

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