Advertisements
Advertisements
Question
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.
Advertisements
Solution
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.
APPEARS IN
RELATED QUESTIONS
Find, which of the following sequence from a G.P. :
8, 24, 72, 216, .............
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
Q 2
Find the sum of G.P. :
`(x + y)/(x - y) + 1 + (x - y)/(x + y) + ..........` upto n terms.
Find the geometric mean between `4/9` and `9/4`
Find the geometric mean between 2a and 8a3
Q 2
The first term of a G.P. is –3 and the square of the second term is equal to its 4th term. Find its 7th term.
Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.
