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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
Find, which of the following sequence from a G.P. :
8, 24, 72, 216, .............
Which term of the G.P.:
`-10, 5/sqrt(3), -5/6,....` is `-5/72`?
Find the geometric progression with 4th term = 54 and 7th term = 1458.
The fourth term, the seventh term and the last term of a geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and number of terms.
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
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 1.2
Q 6
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
