The sequence log a, log frac{a^2}{b}, log fra | vedclass

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(B) Let the terms of the sequence be $T_1, T_2, T_3, \ldots$ where $T_1 = \log a$,$T_2 = \log \frac{a^2}{b}$,and $T_3 = \log \frac{a^3}{b^2}$.Using th

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an $A$.$P$.

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(B) Let the terms of the sequence be $T_1, T_2, T_3, \ldots$ where $T_1 = \log a$,$T_2 = \log \frac{a^2}{b}$,and $T_3 = \log \frac{a^3}{b^2}$.Using the logarithmic property $\log \frac{x}{y} = \log x - \log y$ and $\log x^n = n \log x$:$T_1 = \log a$$T_2 = \log a^2 - \log b = 2 \log a - \log b$$T_3 = \log a^3 - \log b^2 = 3 \log a - 2 \log b$Now,check the common difference $d = T_2 - T_1 = (2 \log a - \log b) - \log a = \log a - \log b$.Check $T_3 - T_2 = (3 \log a - 2 \log b) - (2 \log a - \log b) = \log a - \log b$.Since $T_2 - T_1 = T_3 - T_2$,the sequence is an $A$.$P$. with common difference $d = \log a - \log b$.

The sequence $\log a, \log \frac{a^2}{b}, \log \frac{a^3}{b^2}, \ldots$ is

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