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प्रश्न
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `a/x + c/y = 2`
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उत्तर
a, b and c are in G.P.
`=>` b2 = ac
a, x, b, y and c are in A.P.
`=>` 2x = a + b `=> x = (a + b)/2`
2b = x + y `=> b = (x + y)/2`
2y = b + c `=> y = (b + c)/2`
Now,
`a/x + c/y = (2a)/(a + b) + (2c)/(b + c)`
= `(2a(b + c) + 2c(a + b))/((a + b)(b + c))`
= `(2ab + 2ac + 2ac + 2bc)/(ab + ac + b^2 + bc)`
= `(2ab + 4ac + 2bc)/(ab + b^2 + b^2 + bc)`
= `(2(ab + 2ac + bc))/(ab + 2b^2 + bc)`
= `(2(ab + 2ac + bc))/(ab + 2ac + bc)`
= 2
संबंधित प्रश्न
Find, which of the following sequence from a G.P. :
`1/8, 1/24, 1/72, 1/216, ................`
Which term of the G.P.:
`-10, 5/sqrt(3), -5/6,....` is `-5/72`?
Q 5
If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P.
Show that : x2, b2, y2 are in A.P.
Find the sum of G.P. :
`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms.
How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?
Q 2
Q 3.3
Q 7
Find the 5th term of the G.P. `5/2, 1, .........`
