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If A and G be A.M. and G.M., respectivel...

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are `A pm sqrt((A+G )(A−G ))` .

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PATHFINDER-SAME SPECIAL SEQUENCE-QUESTION BANK
  1. The sum of three numbers in A.P is 12 and sum of their cubes is 288. F...

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

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  3. If the P^(th)and q^(th)terms of an A.Pare a and b respectively,then sh...

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  4. If s1 be the sum of (2n+1) terms of an A.P and s2 be the sum its odd t...

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  5. The ratio if the sum of n terms of two A.P,s is (7n+1):(4n+27). Find t...

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  6. If a^2, b^2, c^2 are in A.P , then prove that 1/(b+c), 1/(c+a),1/(a+b)...

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  7. Find the sum of the following series 6+66+666+..........to n term

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  8. If the first and the n^("th") term of a G.P. are a and b, respectivel...

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  9. Find the equations of the lines, which cut-off intercepts on the axes ...

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  10. If S1, S2 and S3 be respectively the sum of n, 2n and 3n terms of a G....

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  11. If S be the sum. P be the product,and R the sum of the reciprocals of ...

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  12. If x = 1+a+a^2+..........oo where abs(a)lt1 and y=1+b+b^2+........oowh...

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  13. Prove that : (2^(1/4)cdot4^(1/8)cdot8^(1/16)cdot16^(1/32)......oo)=2

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

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  15. Insert 4 arithmetic mean between 5 and 20.

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  16. If n is a even number, find the sum of the series upto n terms1^2-2^2+...

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  17. Find the sum of the following series : 1+5+12+22+35+…. to n terms.

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  18. Sum the following series to n terms 5+7+13+31+85+.......

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  19. If f is a function satisfying f(x+y)= f(x)f(y) for all x,y inN which t...

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  20. If A and G be A.M. and G.M., respectively between two positive numbers...

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