Consider the following statements: 1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP. 2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP. Which of the above statements is/are correct?
Both 1 and 2
Concept:
Multiplying or dividing by a non-zero number does not change the common ratio of a G.P.
Calculation:
Multiplying or dividing by a non-zero number does not change the common ratio of a G.P.
Let the sequence a1, a2, a3 …. an be a G.P.
Common ratio = r = \(\rm a_2\over a_1\) = \(\rm a_3\over a_2\) = \(\rm a_n\over a_{n-1}\)
If each term is multiplied/divided by the same non-zero number, the r value will remain the same. Thus, the sequence will not change.
Similar Questions
If g is the geometric mean of 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, then which one of the following is correct?
What is the greatest value of the positive integer n satisfying the condition \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots + \frac{1}{{{2^{{\rm{n}} - 1}}}} < 2 - \frac{1}{{1000}}?\)
A geometric progression (GP) consists of 200 terms. If the sum of odd terms of the GP is m, and the sum of even terms of the GP is n, then what is its common ratio?
If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is
If m is the geometric mean of \({\left( {\frac{{\rm{y}}}{{\rm{z}}}} \right)^{\log \left( {{\rm{yz}}} \right)}},{\rm{\;}}{\left( {\frac{{\rm{z}}}{{\rm{x}}}} \right)^{\log \left( {{\rm{zx}}} \right)}}{\rm{\;and\;}}{\left( {\frac{{\rm{x}}}{{\rm{y}}}} \right)^{\log \left( {{\rm{xy}}} \right)}}\) then what is the value of m?
The value of the infinite product \({6^{\frac{1}{2}}} \times {6^{\frac{1}{2}}} \times {6^{\frac{3}{8}}} \times {6^{\frac{1}{4}}} \times \ldots \) is
The geometric mean of the observations x 1, x 2, x 3, … x nis G 1. The geometric mean of the observations y 1, y 2, y 3,… y nis G 2. The geometric mean of observations \(\frac{{{{\rm{x}}_1}}}{{{{\rm{y}}_1}}},\frac{{{{\rm{x}}_2}}}{{{{\rm{y}}_2}}},\frac{{{{\rm{x}}_3}}}{{{{\rm{y}}_3}}}, \ldots \frac{{{{\rm{x}}_{\rm{n}}}}}{{{{\rm{y}}_{\rm{n}}}}}\) is
If p, q, r are in one geometric progression and a, b, c are in another geometric progression, then ap, bq, cr are in
What is the sum of the series 0.5 + 0.55 + 0.555 + … to n terms?
Let t1, t2, t3 ... be in GP. What is \(\rm \left(t_1 t_3 \ldots t_{21}\right)^{\frac{1}{11}}\) equal to ?
Important Questions from Geometric Progressions
If g is the geometric mean of 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, then which one of the following is correct?
What is the greatest value of the positive integer n satisfying the condition \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots + \frac{1}{{{2^{{\rm{n}} - 1}}}} < 2 - \frac{1}{{1000}}?\)
The sum of even numbers from 1 to 40 is:
The minimum value of the sum of real numbers a-5, a-4, 3a-3, 1, a8 and a10 with a > 0 is:
The arithmetic mean, geometric mean and median of six positive numbers a, a, b, b, c, c where a < b < c are \(\frac 7 3,\) 2, 2 respectively. Then what is the sum of the squares of all the six numbers?
