Advertisements
Advertisements
प्रश्न
For what values of x, the numbers `-2/7, x, -7/2` are in G.P?
Advertisements
उत्तर
The given numbers are `(-2)/7, x, (-7)/2`
Common ratio = `x/(-2/7) = (-7x)/(2)`
Also, common ratio = `(-7/2)/(x) = (-7)/(2x)`
∴ `(-7x)/2 = (-7)/(2x)`
= `x^2 = (-2 xx 7)/(-2 xx 7) = 1`
= x = `sqrt1`
= x = ± 1
Thus, for x = ± 1, the given numbers will be in G.P.
APPEARS IN
संबंधित प्रश्न
Which term of the following sequence:
`2, 2sqrt2, 4,.... is 128`
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the 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.
If a and b are the roots of are roots of x2 – 3x + p = 0 , and c, d are roots of x2 – 12x + q = 0, where a, b, c, d, form a G.P. Prove that (q + p): (q – p) = 17 : 15.
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
Which term of the G.P. :
\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, \frac{1}{4\sqrt{2}}, . . . \text { is }\frac{1}{512\sqrt{2}}?\]
Which term of the G.P. :
\[2, 2\sqrt{2}, 4, . . .\text { is }128 ?\]
If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.
The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.
Find the sum of the following geometric progression:
(a2 − b2), (a − b), \[\left( \frac{a - b}{a + b} \right)\] to n terms;
Find the sum of the following series:
0.5 + 0.55 + 0.555 + ... to n terms.
Find the rational numbers having the following decimal expansion:
\[0 .\overline {231 }\]
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
The sum of first two terms of an infinite G.P. is 5 and each term is three times the sum of the succeeding terms. Find the G.P.
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. Find the numbers.
If a, b, c are in G.P., prove that:
\[a^2 b^2 c^2 \left( \frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} \right) = a^3 + b^3 + c^3\]
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 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.
If a, b, c are in A.P. and a, b, d are in G.P., then prove that a, a − b, d − c are in G.P.
Find the geometric means of the following pairs of number:
a3b and ab3
Find the geometric means of the following pairs of number:
−8 and −2
If a = 1 + b + b2 + b3 + ... to ∞, then write b in terms of a.
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is
Which term of the G.P. 5, 25, 125, 625, … is 510?
For what values of x, the terms `4/3`, x, `4/27` are in G.P.?
Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.
If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.
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.
The sum of an infinite G.P. is 5 and the sum of the squares of these terms is 15 find the G.P.
Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.
The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio is ______.
Answer the following:
Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`
Answer the following:
Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.
Answer the following:
For a sequence Sn = 4(7n – 1) verify that the sequence is a G.P.
Answer the following:
For a G.P. if t2 = 7, t4 = 1575 find a
Answer the following:
Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.
In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.
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 ______.
