Advertisements
Advertisements
Question
For what values of x, `4/3, x, 4/27` are in G.P.?
Solution
`4/3, x, 4/27` are in geometric progression.
∴ `"t"_2/"t"_1 = "t"_3/"t"_2`
∴ `x/(4/3) = (4/27)/x`
∴ x2 = `4/3 xx 4/27`
∴ x2 = `16/81`
∴ x = `± 4/9`
APPEARS IN
RELATED QUESTIONS
Verify whether the following sequence is G.P. If so, find tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5)), ...`
For a G.P. a = `4/3 and "t"_7 = 243/1024`, find the value of r.
For a sequence, if tn = `(5^("n" - 2))/(7^("n" - 3))`, verify whether the sequence is a G.P. If it is a G.P., find its first term and the common ratio.
Find three numbers in G.P., such that their sum is 35 and their product is 1000.
In a G.P., if t2 = 7, t4 = 1575, find r.
Find k so that k – 1, k, k + 2 are consecutive terms of a G.P.
If pth, qth and rth terms of a G.P. are x, y, z respectively, find the value of xq – r .yr – p .zp – q.
If for a sequence, `t_n = (5^(n-3))/(2^(n-3))`, show that the sequence is a G.P. Find its first term and the common ratio.
Verify whether the following sequences are G.P. If so, find tn.
`sqrt5, 1/sqrt5, 1/(5sqrt5), 1/(25sqrt5),...`
Verify whether the following sequences are G.P. If so, find tn.
`sqrt5, 1/sqrt5, 1/(5sqrt5), 1/(25sqrt5), ...`
For the G.P. if a = `2/3`, t6 = 162 , find r.
For the G.P. if a = `2/3 , t_6 = 162 ` , find r
Verify whether the following sequence are G.P. If so, find tn
`sqrt5, 1/sqrt5, 1/(5sqrt5), 1/(25sqrt5),.......`
For the G.P. if a = `2/3`, t6 = 162, find `r`
Verify whether the following sequence is G.P. If so, find tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5)), ...`
Verify whether the following sequence is G.P. If so, find tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt5), ...`
If for a sequence, `t_n = (5^(n - 3))/(2^(n - 3))`, show that the sequence is a G.P.
Find its first term and the common ratio.
