A sequence log a- log a-2-b- log a-3-b-2 is -where a -b

Explanation for the correct option:Step 1. Write the terms of the given series.log a, loga^2/b, loga^3/b^2…a_1 = log aa_2 = loga^2/b = 2log a – log ba_3 = ...

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Byju's Answer

Standard IX

Mathematics

Sum of n Terms

A sequence lo...

Question

A sequence $\log a$ , $\log \frac{a^{2}}{b}$ , $\log \frac{a^{3}}{b^{2}}$ is ...where $a \neq b$

$A P$

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$G P$

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$H P$

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$n o n e o f t h e s e$

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Solution

The correct option is A
$A P$

Explanation for the correct option:
Step 1. Write the terms of the given series.
$\log a, \log \frac{a^{2}}{b}, \log \frac{a^{3}}{b^{2}} \dots$
$a_{1} = \log a$
$a_{2} = \log \frac{a^{2}}{b}$
$= 2 \log a - \log b$
$a_{3} = \log \frac{a^{3}}{b^{2}}$
$= 3 \log a - 2 \log b$
Step 2. Find the common difference.
$\Rightarrow a_{2} - a_{1} = 2 \log a - \log b - \log a$
$= \log a - \log b$ …..(1)
and $a_{3} - a_{2} = 3 \log a - 2 \log b - 2 \log a + \log b$
$\Rightarrow$ $a_{3} - a_{2} = \log a - \log b$ …..(2)
Step 3. Compare equation (1) and (2):
$\Rightarrow a_{2} - a_{1} = a_{3} - a_{2}$
So the given series is an AP.
Hence, Option ‘A’ is Correct.

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A sequence loga, loga2b, loga3b2 is ...where a≠b

A sequence $\log a$ , $\log \frac{a^{2}}{b}$ , $\log \frac{a^{3}}{b^{2}}$ is ...where $a \neq b$