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If in an A.P. the sum of m terms is equa...

If in an A.P. the sum of `m` terms is equal to `n` and the sum of `n` terms is equal to `m` then prove that the sum of `(m+n)` terms is `-(m+n)`

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If in an A.P. the sum of m terms is equal of n and the sum of n terms is equal to m , then prove that the sum of -(m+n) terms is (m+n) .

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. Find the middle term of the A.P. 213, 205, 197, ..., 37.

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  2. If in an A.P. the sum of m terms is equal to n and the sum of n terms ...

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  3. If the m^(t h) term of an A.P. is 1/n and the n^(t h) terms is 1/m , s...

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  4. Find the 0 where the AP is 40,37,...

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  5. Find whether 0 (zero) is a term of the AP 40, 37, 34, 31, ...

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  6. If 1/(x+2),1/(x+3),1/(x+5) are in A.P. Then, x=

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  7. Find the number of natural numbers between 101 and 999 which are di...

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  8. The sum of first 6 terms of an arithmetic progression is 42. The ratio...

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  9. Find the sum of first 20 terms of an A.P., in which 3rd term is 7 a...

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  10. The sum of 5th and 9th terms of AP is 30. If its 25th term is three...

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  11. The sum of three numbers in A.P. is 12 and the sum of their cubes is ...

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  12. In an A.P., the sum of first n terms is (3n^2)/2+(5n)/2dot Find its 25...

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  13. If Sn , the sum of first n terms of an A.P., is given by Sn=5n^2+3n , ...

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  14. Find the sum of all natural numbers between 250 and 1000 which are ...

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  15. The sum of the first p , q , r terms of an A.P. are a , b , c respecti...

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  16. If m times the m^(t h) term of an A.P. is equal to n times its n^(t h)...

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  17. If the p^(t h) term of an A.P. is q and the q^(t h) term is p , prove ...

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  18. If mth term of an AP is 1/n and its nth term is 1/m , then show that i...

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  19. For the following arithmetic progressions write the first term and ...

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  20. Is 184 a term of the sequence 3,7,11, ... ?

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