Advertisements
Advertisements
Question
Find, which of the following sequence from a G.P. :
`1/8, 1/24, 1/72, 1/216, ................`
Advertisements
Solution
Given sequence: `1/8,1/24,1/72,1/216, ................`
Now,
`(1/24)/(1/8) = 1/3, (1/72)/(1/24) = 1/3, (1/216)/(1/72) = 1/3`
Since `(1/24)/(1/8) = (1/72)/(1/24) = (1/216)/(1/72) = .......... = 1/3,` the given sequence is a G.P. with common ratio `1/3`.
RELATED QUESTIONS
Find the G.P. whose first term is 64 and next term is 32.
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.
The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : q2 = pr.
Q 7
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
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.
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 geometric mean between 2a and 8a3
Q 8
Find the 5th term of the G.P. `5/2, 1, .........`
