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Insert 10 arithmetic means between 2 and...

Insert 10 arithmetic means between 2 and 57.

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Insert 5 arithmetic means between 8 and 26.

Insert 6 arithmetic means between 3 and 24.

Insert 3 arithmetic means between : 5 and 21.

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Insert 4 geometric means between 6 and 192.

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Let A_(1),A_(2),A_(3),"......."A_(m) be arithmetic means between -3 and 828 and G_(1),G_(2),G_(3),"......."G_(n) be geometric means between 1 and 2187. Product of geometric means is 3^(35) and sum of arithmetic means is 14025. The value of n is

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Insert 5 arithmetic means between 8 and 26.

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  2. Insert 6 arithmetic means between 3 and 24.

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  3. Insert 10 arithmetic means between 2 and 57.

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

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

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

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

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

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

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

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  11. 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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  12. 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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  13. 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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  14. Between 1 and 31, n A.M's have been inserted in sucha a way that the r...

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

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

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

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

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

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

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