Question:
The sequence $\log \,a$, $\log \frac{a^{2}}{b}, \,\log \frac{a^{3}}{b^{2}}, ...........$ is
The sequence $\log \,a$, $\log \frac{a^{2}}{b}, \,\log \frac{a^{3}}{b^{2}}, ...........$ is
Updated On: Jul 25, 2024
- a G.P.
- an A.P.
- a H.P.
- both a G.P. and a H.P
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Let $S=\log a, \log \frac{a^{2}}{b}, \log \frac{a^{3}}{b^{2}}, \ldots$
$=\log a,(2 \log a-\log b) (3 \log a-2 \log b)$,
Now, $T_{2}-T_{1}=\log a-\log b$
and $T_{3}-T_{2}=\log a-\log b$
Hence, it is an AP.
Was this answer helpful?
0
0
Top Questions on sequences
- 10, 30, 68, 130, ___ ,350
find the missing number? - Using mathematical induction, the numbers $ a_n $ are defined by $ a_0 = 1, a_{n+1} = 3n^2 + n + a_n, (n \geq 0) $. Then, $ a_n $ is equal to
If aa is the greatest term in the sequence \(a_n=\frac{n^3}{n^4+147},n=1,2,3,...,\) then a is equal to______________.
- The statement $(p \wedge(\sim q)) \Rightarrow(p \Rightarrow(\sim q))$ is
The sum\(\displaystyle\sum_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}\) is equal to:
View More Questions
Questions Asked in WBJEE exam
- If 1000! = 3n × m, where m is an integer not divisible by 3, then n =?
- WBJEE - 2024
- Probability
- Chords AB CD of a circle intersect at right angle at the point P. If the lengths of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is:
- If the relation between the direction ratios of two lines in \(\mathbb{R}^3\) are given by \(l + m + n = 0\), \(2lm + 2mn - ln = 0\), then the angle between the lines is:
- WBJEE - 2024
- Vectors
- If \(a, b, c\) are distinct odd natural numbers, then the number of rational roots of the equation \(ax^2 + bx + c = 0\) is:
- WBJEE - 2024
- Quadratic Equation
- What force \(F\) is required to start moving this 10 kg block shown in the figure if it acts at an angle of \(60^\circ\) as shown? (\(\mu_s = 0.6\)).
- WBJEE - 2024
- laws of motion
View More Questions
Concepts Used:
Sequences
A set of numbers that have been arranged or sorted in a definite order is called a sequence. The terms in a series mention the numbers in the sequence, and each term is distinguished or prominent from the others by a common difference. The end of the sequence is frequently represented by three linked dots, which specifies that the sequence is not broken and that it will continue further.
Read More: Sequence and Series
Types of Sequence:
There are four types of sequences such as:
- Arithmetic Sequence
- Fibonacci Sequence
- Geometric Sequence
- Harmonic Sequence