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If (1)/(x) , (1)/(y) , (1)/(z) are A.P. ...

If `(1)/(x) , (1)/(y) , (1)/(z)` are A.P. show that
xy,zx,yz are in A.P.

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If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that (y+z)/(x) , (z+x)/(y) , (x+y)/(z) are in A.P.

If a^((1)/(x))= b^((1)/(y))= c^((1)/(z)) and a,b,c are in G.P., prove that x,y,z are in A.P.

The value of x + y + z is 15 if a, x, y, z, b are in A.P. while the value of (1)/(x) + (1)/(y) + (1)/(z) + (1)/(z) is (5)/(3) if a, x, y, z, b are in H.P. the value of a and b are

Let a(a != 0) is a fixed real number and (a-x)/(px)=(a-y)/(qy)=(a-z)/(rz) . If p, q, r are in A.P., show that 1/x,1/y,1/z are in A.P.

If reciprocals of (y-x),2(y-a), (y-z) are in A.P., prove that x-a,y-a,z-a are in G.P.

1/a, 1/b and 1/c are in A.P. Show that bc, ca, and ab are also in A.P.

If (1)/(x+y), (1)/(2y) , (1)/(y+z) are the three consecutive terms of an A.P. prove that x ,y,z are the three consecutive terms of a G.P.

If (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are also in A.P. (a +b+c != 0) .

If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ b ,\ c are in A.P.

If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ b ,\ c are in A.P.

ICSE-SEQUENCE AND SERIES -EXERCISE 14 (d)
  1. Find the A.M. between: ( cos theta + sin theta )^(2) and ( cos the...

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  2. Find the A.M. between: (x+y)^(2) and (x-y)^(2)

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  3. Insert : (i) 3 arithmetic means between 5 and 17 . (ii) 4 arithmet...

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  4. Find two numbers whose product is 91 and whose A.M. is 10.

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  5. If p arithmetic means are inserted between a and b, prove that d = (b-...

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  6. The sum of three numbers in A.P. is 33, and the sum of their squares i...

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  7. There are four numbers in A. P., the sum of the two extremes is 8, and...

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

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  9. The angles of a triangle are in A.P. If the greatest angle is double t...

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  10. The sum of the first three consecutive terms of an A.P. is 9 and the s...

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  11. a(1),a(2),a(3),a(4),a(5), are first five terms of an A.P. such that a(...

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  12. The angles of a quadrilateral are in A.P. and the greatest angle is do...

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  13. If a,b,c are in A.P. show that a((1)/(b)+(1)/(c)),b((1)/(c)+(1)/(a))...

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  14. If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that xy,zx,yz are in A....

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  15. If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that xy,zx,yz are in A....

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  16. If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that (y+z)/(x) , (z+x)/...

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  17. If (b+c)^(-1), (c+a)^(-1), (a+b)^(-1) are in A.P. then show that (a)/(...

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  18. If (b+c-a)/(a) , (c+a-b)/(b) , (a+b-c)/(c) are in A.P. then prove that...

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  19. If x ,y,z are in A.P. show that (xy)^(-1) , (zx)^(-1) , (yz)^(-1) are ...

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  20. If a^(2) , b^(2) , c^(2) are in A.P , pove that a/(a+c) , b/(c+a) ,...

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