Advertisements
Advertisements
प्रश्न
The numbers 3, x, and x + 6 form are in G.P. Find x
Advertisements
उत्तर
The numbers 3, x, and x + 6 are in G.P.
∴ `"x"/3 = ("x" + 6)/"x"`
∴ x2 = 3x + 18
∴ x2 – 3x – 18 = 0
∴ (x – 6)(x + 3) = 0
∴ x – 6 = 0 or x + 3 = 0
∴ x = 6 or x = – 3
APPEARS IN
संबंधित प्रश्न
Which term of the following sequence:
`sqrt3, 3, 3sqrt3`, .... is 729?
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)th to (2n)th term is `1/r^n`.
Find the value of n so that `(a^(n+1) + b^(n+1))/(a^n + b^n)` may be the geometric mean between a and b.
Show that one of the following progression is a G.P. Also, find the common ratio in case:
4, −2, 1, −1/2, ...
Find:
the ninth term of the G.P. 1, 4, 16, 64, ...
Find :
the 8th term of the G.P. 0.3, 0.06, 0.012, ...
If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.
Find three numbers in G.P. whose sum is 38 and their product is 1728.
Find the sum of the following geometric series:
\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]
Find the sum of the following series:
9 + 99 + 999 + ... to n terms;
Find the sum of the following serie to infinity:
\[1 - \frac{1}{3} + \frac{1}{3^2} - \frac{1}{3^3} + \frac{1}{3^4} + . . . \infty\]
Find the rational numbers having the following decimal expansion:
\[0 . 6\overline8\]
One side of an equilateral triangle is 18 cm. The mid-points of its sides are joined to form another triangle whose mid-points, in turn, are joined to form still another triangle. The process is continued indefinitely. Find the sum of the (i) perimeters of all the triangles. (ii) areas of all triangles.
If a, b, c are in G.P., prove that:
(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.
If a, b, c, d are in G.P., prove that:
\[\frac{ab - cd}{b^2 - c^2} = \frac{a + c}{b}\]
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
If a, b, c, d are in G.P., prove that:
(a2 + b2), (b2 + c2), (c2 + d2) are in G.P.
If a, b, c, d are in G.P., prove that:
(a2 + b2 + c2), (ab + bc + cd), (b2 + c2 + d2) are in G.P.
If the 4th, 10th and 16th terms of a G.P. are x, y and z respectively. Prove that x, y, z are in G.P.
Insert 6 geometric means between 27 and \[\frac{1}{81}\] .
Insert 5 geometric means between 16 and \[\frac{1}{4}\] .
Find the geometric means of the following pairs of number:
a3b and ab3
If the first term of a G.P. a1, a2, a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is
Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after 10 years.
Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after n years.
For the following G.P.s, find Sn
3, 6, 12, 24, ...
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]
Express the following recurring decimal as a rational number:
`0.bar(7)`
Find : `sum_("r" = 1)^oo 4(0.5)^"r"`
Select the correct answer from the given alternative.
Which term of the geometric progression 1, 2, 4, 8, ... is 2048
Answer the following:
For a G.P. if t2 = 7, t4 = 1575 find a
Answer the following:
If for a G.P. t3 = `1/3`, t6 = `1/81` find r
Answer the following:
Find k so that k – 1, k, k + 2 are consecutive terms of a G.P.
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
Answer the following:
If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in ______.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
