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If (b+c-a)/a,(c+a-b)/b,(a+b-c)/c are in ...

If `(b+c-a)/a,(c+a-b)/b,(a+b-c)/c` are in A.P, prove that `1/a,1/b,1/c`are also A.P.s

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Suppose (b+c)/a,(c+a)/b,(a+b)/c are in A.P.Prove 1/a,1/b,1/c are also A.P.

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If (b-c)^(2) , (c-a)^(2), (a-b)^(2) are in A.P. then prove that (1)/(b-c) , (1)/(c-a), (1)/(a-b) are also in A.P.

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Suppose that a, b, c are in A.P. Prove that 2b = a + c

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A N EXCEL PUBLICATION-SEQUENCES AND SERIES-QUESTION BANK
  1. The sum of three numbers in A.P. is -3,'and their product is 8. Find t...

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  2. If a, b, c are in A.P, prove that 1/(bc),1/(ca),1/(ab) are also in A.P...

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  3. If (b+c-a)/a,(c+a-b)/b,(a+b-c)/c are in A.P, prove that 1/a,1/b,1/care...

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  4. Find the sum of odd integers from 1 to 2001

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  5. Find the sum of all natural numbers between 100 and 1000 which are mul...

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

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  7. How many terms of the A.P,-6 ,-11/2,-5,...are needed to give the sum -...

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  8. If the m^th terms of an AP is 1/n and the n^th term is 1/m, prove that...

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  9. If the sum of certain number of terms of the AP 25,22,19,........is 11...

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  10. Find the sum of n terms of the AP, whose K^th term is ak=5K+1.

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  11. If the sum of n terms of an A.P. is pn+qn^2, where p and q are constan...

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  12. The sums of n terms of two A.P.s are in the ratio (5n + 4): (9n + 6). ...

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  13. If the sum of p terms of an AP is the same as the sum of its q terms, ...

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  14. The sum of the first p,q,r terms of an AP are a,b,c respectively, prov...

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  15. The ratio of the sums of m and n terms of an A.P is m^2:n^2. Show that...

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  16. If the sum of n terms of an A.P is 3n^2+5n and its m^(th) term is 164....

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  17. Insert five numbers between 8 and 26 such that the resulting sequence...

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  18. If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, find the v...

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  19. Between 1 and 31, m numbers have been inserted in such a way that the ...

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  20. A man starts repaying a loan as a first instalment of Rs. 100. If he i...

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