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Insert seven A.M.’s between 1 and 41....

Insert seven A.M.’s between 1 and 41.

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By inserting eight A.M.’s between 2 and 29 prove that the sum of the eight A.M's is equal to eight times of A.M. of 2 and 29.

Determine p A.M.’s between 1 and p^2 .

There are n A.M.'s between 1 and 51 and fourth mean : seventh mean = 3 : 5, Determine n.

Inserting three G.M.'s between 1/9 and 9 verify that their product is equal to cube of G.M. of 1/9 and 9.

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KALYANI PUBLICATION-PROGRESSION-EXERCISE
  1. Insert three arithmetic mean between 2 and 14.

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  2. Insert three A.M.'s between 3 1/4 and 1 1/4.

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  3. Insert seven A.M.’s between 1 and 41.

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  4. Insert five A.M.'s between 1.2 and 8.4.

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  5. Determine four numbers between 7 and 4 such that these six numbers are...

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  6. Determine three quantities between x and 9x+ 4 such that these five nu...

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  7. Determine p A.M.’s between 1 and p^2.

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

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  9. If (a^(n+1)+b^(n+1))/(a^n+b^n) is the A.M. of a and b, then find n.

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  10. There are n A.M.'s between 5 and 35. If second mean : last mean = 1 ...

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  11. There are n A.M.'s between 1 and 51 and fourth mean : seventh mean =...

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  12. There are p A.M.'s between 5 and 41 and third mean : (p-1)th mean = 2 ...

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  13. The product of two numbers is 16. The product of two A.M.’s between th...

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  14. If a1, a2, a3…..an are in AP, then prove that frac(1)(a1 a2)+frac(1)(a...

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  15. Find the sum of the following series up to the specified term 1 + ...

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  16. Find the sum of the following AP up to the specified term 2 + 6 + ...

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  17. Find the sum of the following AP up to the specified term 20+ 18+ ...

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  18. Find the sum of the following AP is up to the specified term 4+7+1...

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  19. Find the sum of the following AP up to the specified term 1/2+1/3+...

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  20. Find the sum of the following series up to the specified term sqrt...

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