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If A is the A.M. between a and b, prove ...

If A is the A.M. between a and b, prove that :
`(A-a)^(2) +(A-b)^(2)=1/2(a-b)^(2) `.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Insert 6 arithmetic means between 3 and 24.

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  2. Insert 10 arithmetic means between 2 and 57.

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  3. If A is the A.M. between a and b, prove that : (A-a)^(2) +(A-b)^(2)=...

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  4. If A is the A.M. between a and b, prove that : 4(a-A)(A-b)=(a-b)^(2...

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  5. If A1 and A2 are two A.M.’s between a and b, prove that : (2A1-A2)(2...

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  6. If A1 and A2 are two A.M.’s between a and b, prove that : A1+A2 =a+b...

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  7. Insert 10 A.M.’s between 5 and -17 and prove that their sum is ten tim...

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  8. n arithmetic means are inserted between 3 and 17 such that ratio of fi...

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  9. If a, b, c are in A.P., then prove that : (a-c)^2 =4(b^2 -ac).

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  10. If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2).

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  11. Find the value of n so that (a^(n+1)+ b^(n+1))/(a^n+b^n) may be the ge...

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

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  13. Between 1 and 31, n A.M's have been inserted in sucha a way that the r...

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  14. Find three numbers in A.P. : whose sum is 21 and product is 315.

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  15. Find three numbers in A.P. : whose sum is 24 and Product is 440.

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  16. The sum of the first three terms of an A.P. is 36 while their product ...

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  17. The sum of three Consecutive terms of an A.P. is 15 and sum of their S...

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  18. The sum of three consecutive terms of an A.P. is 9 and the sum of thei...

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  19. Split 69 into three parts in A.P. such that the product of the two sma...

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  20. Solve the equation : 1+6+11+ 16+.....+x= 148

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