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

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 in A.P.

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. How many terms are there in the A.P. 3, 7, 11, ... 407?

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  2. If a ,b ,c ,d ,e are in A.P., the find the value of a-4b+6c-4d+edot

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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 ...

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  4. If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+(1//a c),...

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  5. Find the degree of the expression (1+x)(1+x^6)(1+x^(11))........(1+x^(...

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  6. In an A.P. of 99 terms, the sum of all the odd-numbered terms is 2550....

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  7. Divide 32 into four parts which are in A.P. such that the ratio of the...

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  8. Show (m+n)th and (m-n)t h terms of an A.P. is equal to twice the mth ...

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  9. If the sum of three consecutive numbers in A.P., is 24 and their pr...

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  10. Prove that the sum of n number of terms of two different A.P. s can be...

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  11. In an A.P. if S1=T1+T2+T3+.....+Tn (n is odd)S2=T2+T4+T6+.........+T(n...

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  12. If the sum of the series 2, 5, 8, 11, ... is 60100, then find the valu...

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

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  14. If eleven A.M. ‘s are inserted between 28 and 10, then find the number...

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

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  16. Find the sum of first 24 terms of the A.P. a1,a2, a3 ......., if it i...

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  17. If the arithmetic progression whose common difference is nonzero the ...

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

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  19. If the first two terms of as H.P. are 2/5 and 12/13, respectively. The...

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  20. Insert five arithmetic means  between 8 and 26. or Insert five numbers...

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