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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 inA.P

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`(b+c-a)/a,(c+a-b)/b,(a+b-c)/c` are in A.P
`rArr{(b+c-a)/a+2},{(c+a-b)/b+2},{(a+b-c)/c+2}`
are in A.P [Adding 2 to each other]
`rArr(a+b+c)/a,(a+b+c)/b,(a+b+c)/c` are in A.P
`rArr 1/a',1/b,1/c` are in A.P. [ Dividing each term by a+b+c]
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if ((b +c -a))/a,((c+a -b))/b, (( a+b -c))/c are in AP, prove that 1/a , 1/b,1/c are in AP.

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

if (1)/(b+c),(1)/(c+a),(1)/(a+b) are in A.P. prove that a^(2),b^(2),c^(2) are also in A.P.

CENGAGE-PROGRESSION AND SERIES-Examples
  1. If p,q and r (pneq) are terms ( not necessarily consecutive) of an A.P...

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  2. If the terms of the A.P. sqrt(a-x),sqrt(x),sqrt(a+x) are all in intege...

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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/c ar...

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

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  5. If a,b,c are in A.P., then prove that the following are also in A.P ...

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  6. If the sum of three numbers in A.P., is 24 and their product is 440...

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

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

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  10. Between 1 and 31 are inserted m arithmetic mean so that the ratio of t...

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  11. find the sum of all three digit natural numbers which are divisible by...

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  12. Find the number of terms in the series 20 ,19 1/3,18 2/3... the sum of...

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  13. Find the degree of the expression (1+x)(1+x^6)(1+x^(11))(1+x^(101))dot

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

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

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  16. If the sequence a(1),a(2),a(3),…,a(n) is an A.P., then prove that a(1)...

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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 n arithmetic means are inserted between 2 and 38, then the sum of t...

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  20. The third term of a geometric progression is 4. Then find the product ...

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