Advertisements
Advertisements
प्रश्न
If a, b and c are in A.P. and also in G.P., show that : a = b = c.
Advertisements
उत्तर
a, b and c are in A.P.
`=>` 2b = a + c
`=> b = (a + c)/2`
a, b and c are also in G.P.
`=>` b2 = ac
`=> ((a + c)/2)^2 = ac`
`=> (a^2 + c^2 + 2ac)/4 = ac`
`=>` a2 + c2 + 2ac = 4ac
`=>` a2 + c2 – 2ac = 0
`=>` (a – c)2 = 0
`=>` a – c = 0
`=>` a = c
Now, 2b = a + c
`=>` 2b = a + a
`=>` 2b = 2a
`=>` b = a
Thus, we have a = b = c
संबंधित प्रश्न
Find the seventh term from the end of the series :
`sqrt(2), 2, 2sqrt(2), ........., 32.`
Q 7
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 a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `1/x + 1/y = 2/b`
Find the sum of G.P. : 3, 6, 12, .........., 1536.
Q 3.2
Q 3.3
Q 8
Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.
