Advertisements
Advertisements
प्रश्न
In a G.P., if t2 = 7, t4 = 1575, find r.
उत्तर
Given t2 = 7, t4 = 1575
tn = arn–1
∴ t2 = ar
∴ 7 = ar
a = `7/"r"` ...(i)
t4 = ar3
∴ ar3 = 1575
∴ `"r"^3 xx (7/"r")` = 1575 ...[From (i)]
∴ r2 x 7 = 1575
∴ r2 = `1575/7`
∴ r2 = 225
∴ r = ±15
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, find tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5)), ...`
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, r = – 3, find t6.
For what values of x, `4/3, x, 4/27` are in G.P.?
If p, q, r, s are in G. P., show that p + q, q + r, r + s are also in G. P.
For a G.P. a = `4/3 and "t"_7 = 243/1024`, find the value of r.
Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.
For a sequence Sn = 4(7n – 1), verify whether the sequence is a G.P.
Verify whether the following sequences are G.P.If so, find tn.
`sqrt(5),1/sqrt(5),1/(5sqrt(5)),1/(25sqrt(5))`
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.
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 tn:
`sqrt5, 1/sqrt5, 1/(5 sqrt5), 1/(25 sqrt5), ...`
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/(25sqrt5), ...`
