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Find the A.M. between : 6 and -8....

Find the A.M. between :
6 and -8.

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Find the A.M. between : 3.7 and 5.5.

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

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

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

If a,b,c are in AP and p is the AM between a and b and q is the AM between b and c, then show that b is the AM between p and q.

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : a/x+c/y=2 .

The G.M. between -2i and 8i is:

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : 1/x+1/y=2/b .

If the A.M. between pth and qth terms of an A.P. be equal to the A.M. between rth and sth terms of the A.P., show that p +q= r+s.

Insert 3 A.M.’s between 3 and 19.

MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove...

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  2. Find the A.M. between : 3.7 and 5.5.

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  3. Find the A.M. between : 6 and -8.

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  4. Insert 3 arithmetic means between : 3 and 15.

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  5. Insert 3 arithmetic means between : 5 and 21.

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  6. Insert 5 arithmetic means between 8 and 26.

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  7. Insert 6 arithmetic means between 3 and 24.

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  8. Insert 10 arithmetic means between 2 and 57.

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

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

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

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

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

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

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

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  16. 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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  17. 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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  18. 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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  19. Between 1 and 31, n A.M's have been inserted in sucha a way that the r...

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

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