Advertisements
Advertisements
प्रश्न
If p, q, r, s are in G. P., show that p + q, q + r, r + s are also in G. P.
उत्तर
p, q, r, s are in G.P.
∴ `"q"/"p" = "r"/"q" = "s"/"r"`
Let `"q"/"p" = "r"/"q" = "s"/"r"` = k
∴ q = pk, r = qk, s = rk
We have to prove that p + q, q + r, r + s are in G.P.
i.e. to prove that `"q + r"/"p + q" = "r + s"/"q + r"`
L.H.S. = `"q + r"/"p + q" ="q + qk"/"p + pk" = ("q"(1 + "k"))/("p"(1 + "k")) = "q"/"p"` = k
R.H.S. = `"r + s"/"q + r" ="r + rk"/"q + qk" = ("r"(1 + "k"))/("q"(1 + "k")) = "r"/"q"` = k
∴ `"q + r"/"p + q" ="r + s"/"q + r"`
∴ p + q, q + r, r + s are in G.P.
APPEARS IN
संबंधित प्रश्न
Verify whether the following sequence is G.P. If so, write tn:
2, 6, 18, 54, ...
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:
3, 4, 5, 6, ...
Verify whether the following sequence is G.P. If so, write tn:
7, 14, 21, 28, ...
For the G.P., if a = `7/243, "r" = 1/3`, find t3.
For the G.P., if a = 7, r = – 3, find t6.
Find five numbers in G. P. such that their product is 1024 and fifth term is square of the third term.
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),` ....
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`, t6 = 162 , find r.
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),.......`
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/(5sqrt5), 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.
