Advertisements
Advertisements
Question
If a, b and c are in A.P. and also in G.P., show that : a = b = c.
Advertisements
Solution
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
RELATED QUESTIONS
Find, which of the following sequence from a G.P. :
8, 24, 72, 216, .............
Find, which of the following sequence from a G.P. :
9, 12, 16, 24, ................
Find the 9th term of the series :
1, 4, 16, 64, ...............
Find the G.P. whose first term is 64 and next term is 32.
Which term of the G.P.:
`-10, 5/sqrt(3), -5/6,....` is `-5/72`?
Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
Find the seventh term from the end of the series :
`sqrt(2), 2, 2sqrt(2), ........., 32.`
Q 7
Q 1.2
Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.
