Advertisements
Advertisements
प्रश्न
The numbers x − 6, 2x and x2 are in G.P. Find x
Advertisements
उत्तर
The numbers x − 6, 2x and x2 are in G.P.
∴ `(2x)/(x - 6) = x^2/(2x)`
∴ 4x2 = x2(x – 6)
∴ 4 = x – 6 ...[∵ x2 ≠ 0]
∴ x = 10
APPEARS IN
संबंधित प्रश्न
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
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.
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
If a, b, c are in A.P,; b, c, d are in G.P and ` 1/c, 1/d,1/e` are in A.P. prove that a, c, e are in G.P.
Show that one of the following progression is a G.P. Also, find the common ratio in case:1/2, 1/3, 2/9, 4/27, ...
Which term of the G.P. :
\[\frac{1}{3}, \frac{1}{9}, \frac{1}{27} . . \text { . is } \frac{1}{19683} ?\]
Find three numbers in G.P. whose product is 729 and the sum of their products in pairs is 819.
Find the sum of the following geometric progression:
4, 2, 1, 1/2 ... to 10 terms.
Find the sum of the following geometric series:
`sqrt7, sqrt21, 3sqrt7,...` to n terms
The 4th and 7th terms of a G.P. are \[\frac{1}{27} \text { and } \frac{1}{729}\] respectively. Find the sum of n terms of the G.P.
The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.
Find the rational number whose decimal expansion is `0.4bar23`.
If a, b, c, d are in G.P., prove that:
(b + c) (b + d) = (c + a) (c + d)
If a, b, c are in G.P., prove that the following is also in G.P.:
a2, b2, c2
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
If xa = xb/2 zb/2 = zc, then prove that \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
If a, b, c are in A.P. and a, x, b and b, y, c are in G.P., show that x2, b2, y2 are in A.P.
If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
The product (32), (32)1/6 (32)1/36 ... to ∞ is equal to
Mark the correct alternative in the following question:
Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then p2R3 : S3 is equal to
Check whether the following sequence is G.P. If so, write tn.
1, –5, 25, –125 …
Check whether the following sequence is G.P. If so, write tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...
Check whether the following sequence is G.P. If so, write tn.
7, 14, 21, 28, …
For the following G.P.s, find Sn.
p, q, `"q"^2/"p", "q"^3/"p"^2,` ...
The sum of an infinite G.P. is 5 and the sum of the squares of these terms is 15 find the G.P.
The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the perimeters of all the squares
A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball
Select the correct answer from the given alternative.
Which of the following is not true, where A, G, H are the AM, GM, HM of a and b respectively. (a, b > 0)
Answer the following:
Find three numbers in G.P. such that their sum is 35 and their product is 1000
Answer the following:
For a sequence Sn = 4(7n – 1) verify that the sequence is a G.P.
Answer the following:
Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...
Answer the following:
Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`
The third term of a G.P. is 4, the product of the first five terms is ______.
The sum or difference of two G.P.s, is again a G.P.
The sum of the infinite series `1 + 5/6 + 12/6^2 + 22/6^3 + 35/6^4 + 51/6^5 + 70/6^6 + ....` is equal to ______.
The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is ______.
