Advertisements
Advertisements
प्रश्न
Verify whether the following sequence is G.P. If so, write tn:
2, 6, 18, 54, ...
उत्तर
2, 6, 18, 54, ...
t1 = 2, t2 = 6, t3 = 18, t4 = 54, …
Here, `"t"_2/"t"_1 = "t"_3/"t"_2 = "t"_4/"t"_3` = 3
Since, the ratio of any two consecutive terms is a constant, the given sequence is a geometric progression.
Here. a = 2, r = 3
tn= arn–1
∴ tn = 2(3n–1)
APPEARS IN
संबंधित प्रश्न
Verify whether the following sequence is G.P. If so, write tn:
1, – 5, 25, – 125, ...
Verify whether the following sequence is G.P. If so, write tn:
7, 14, 21, 28, ...
For the G.P., if r = `1/3`, a = 9, find t7.
For the G.P., if a = `7/243, "r" = 1/3`, find t3.
For what values of x, `4/3, x, 4/27` are in G.P.?
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.
Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.
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 sequence is G.P. If so, find `"t"_n`
`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.
`sqrt5,1/sqrt5,1/(5sqrt5),1/(25sqrt5),...`
For the G.P., if a = `2/3 , t_6 ` = 162 , find r
For the G.P. if a = `2/3 , t_6 = 162 ` , find r
Verify whether the following sequence is G.P. If to find tn:
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...
For the G.P. if a = `2/3`, t6 = 162, find `r`
Verify whether the following sequence is G.P. If so, find tn.
`sqrt5,1/(sqrt5),1/(5sqrt5), 1/(25sqrt5)`, ......
