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प्रश्न
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.
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उत्तर
a, b and c are in A.P.
`=>` 2b = a + c
a, x and b are in G.P.
`=>` x2 = ab
b, y and c are in G.P.
`=>` y2 = bc
Now,
x2 + y2 = ab + bc
= b(a + c)
= b × 2b
= 2b2
`=>` x2, b2 and y2 are in A.P.
संबंधित प्रश्न
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.
Q 6
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
Q 2
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
Find the sum of G.P. :
`(x + y)/(x - y) + 1 + (x - y)/(x + y) + ..........` upto n terms.
Find the sum of G.P. :
`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms.
Find the geometric mean between `4/9` and `9/4`
Q 2
