In a G.P. the sum of infinite terms is 1...

In a G.P. the sum of infinite terms is 15, the sum of the squares of these terms is 45. Find the G.P.

Text Solution

Verified by Experts

The correct Answer is:

`{5, (10)/(3), (20)/(9), (40)/(27),…oo}`

Topper's Solved these Questions

SEQUENCE AND SERIES
CHHAYA PUBLICATION|Exercise Exercise 9 E (Very Short Answer Type Questions)|28 Videos
SEQUENCE AND SERIES
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (MCQs)|5 Videos
SEQUENCE AND SERIES
CHHAYA PUBLICATION|Exercise Exercise 9 D (Multiple Choice Type Questions)|2 Videos
SECOND ORDER DERIVATIVE
CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Assertion-Reason type)|2 Videos
SET THEORY
CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

The sum of an infinite G.P series is 15 and the sum of the squares of these terms is 45, Find the G.P

If the sum of an infinitely decreasing GP is 3, and the sum of the squares of its items is 9/2, the sum of the cubes of the terms is.

The common ratio of a series in G.P. is 3, the sum of the 1st and 3rd terms is equal to the sum of the squares of the 1st and 2nd terms, find the sum of n terms. If n = 6, show that the sum is 364.

The sum of the first 4 terms of a G.P. is 40 and the sum of first 8 terms is 3280. Obtain the G.P.

The sum of infinite number of terms in G.P. is 20 and the sum of their squares is 100. Then find the common ratio of G.P.

In an infinite G.P., each term is equal to three times the sum of all the terms that follow it and the sum of the first two terms is 15, find the sum of the series to infinity.

The sum of 2n terms of a series in G.P. is 2R and the sum of the reciprocals of those terms is R , find the continued product of the terms.

If the sum of first n terms of G.P. is S and the sum of its first 2n terms is 5S, then show that the sum of its first 3n terms is 21S.

If the sum of an infinite GP is 20 and sum of their square is 100 then common ratio will be=

If the sum of an infinite G.P. series is equal to the sum of 5 times of its odd terms, then the common ratio will be

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 D (Very Short Answer Type Questions)

Find the sum of each of the following infinite geometric series, if it...
Text Solution
|
Express each of the following recurring decimals in the form of an inf...
Text Solution
|
Express each of the following recurring decimals in the form of an inf...
Text Solution
|
Express each of the following recurring decimals in the form of an inf...
Text Solution
|
Express each of the following recurring decimals in the form of an inf...
Text Solution
|
Express 0.overset(.)4 as an infinite geometric series and hence prove ...
Text Solution
|
The sum of an infinite geometric series is (1)/(3) and its first terms...
Text Solution
|
The sum of an infinite geometric series is 6 and the sum of its first ...
Text Solution
|
In a G.P. the sum of infinite terms is 15, the sum of the squares of t...
Text Solution
|
Two infinite geometric series starts from the same number. If the comm...
Text Solution
|
The distance passed over by a certain pendulum bob in succeeding swing...
Text Solution
|
In an infinite G.P., each term is equal to three times the sum of all ...
Text Solution
|
If x = a + (a)/(r ) + (a)/(r^(2))+…oo (-1 lt (1)/(r ) lt 1), y = b -...
Text Solution
|
If |a| lt 1, |b| lt 1, then show that a(a+b) + a^(2) (a^(2) + b^(2))...
Text Solution
|
If, for real numbers a, b, c, r with |r| gt 1, x = a + (a)/(r ) + (a)/...
Text Solution
|
If for two reals a, b, with |a| gt 1, |b| gt 1, x = 1 + (1)/(a) + (1)/...
Text Solution
|
For a real number 'a' with |a| lt 1, if x = a - a^(3) + a^(5)-…, y = 1...
Text Solution
|
For a real number a with 0 lt a lt (1)/(2), if b = 1 - a + a^(2) - a^(...
Text Solution
|
If, for 0 lt a lt (1)/(2), the sum of series a+a^(2) + a^(3)+… is b, t...
Text Solution
|
If x = underset(n = 0)overset(oo)Sigma cos^(2n)theta, " " y = underset...
Text Solution
|