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If in an A.P, Sn=n^2p and Sm=m^2p, then ...

If in an A.P, `S_n=n^2p` and `S_m=m^2p`, then `S_p` is equal to

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Let first term = a and Common difference = d
According to the question,
`S_n = n^2 p `
`=> S_n = n/2 (2a + (n–1) d)= n^2p `
...
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. The first term of an A.P.is 2 and the last term is 50. the sum of all ...

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  2. The number of terms of an A.P. is even, the sum of odd terms is 24, of...

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  3. If in an A.P, Sn=n^2p and Sm=m^2p, then Sp is equal to

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  4. If 12th term of an A.P. is -13 and the sum of the first four terms i...

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  5. If the 5th and 12th terms of an A.P. are 30 and 65 respectively, wha...

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  6. Find the sum of n terms of an A.P. whose kth terms is 5k+1.

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  7. Sum of all two digit numbers which when divided by 4 yield unity as re...

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  8. If the sum of a certain number of terms of the AP 25,22,19... is 116. ...

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  9. How many terms of the A.P. -6, -(11)/2,\ -5,... are needed to give the...

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  10. In an A.P. the first term is 2 and the sum of the first five terms is ...

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  11. If Sn=n P+(n(n-1))/2Q ,w h e r eSn denotes the sum of the first n term...

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  12. The sum of n terms of two arithmetic progressions are in the ratio 5n+...

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  13. If 2/3, k ,5/8 are in A.P., find the value of kdot

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  14. If 1/a ,1/b ,1/c are in A.P. prove that: (b+c)/a ,(c+a)/b ,(a+b)/c are...

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  15. If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) ...

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  16. If a, b, c are in A.P, then show that: b+c-a , c+a-b , a+b-c are in A....

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  17. If a, b, c are in A.P, then show that: b c-a^2, c a-b^2,a b-c^2 are i...

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  18. If (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are als...

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  19. If (b+c)/a ,(c+a)/b ,(a+b)/c are in A.P., prove that : b c ,\ c a ,\ a...

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  20. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

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