If a_1, a_2, a_3, ldots, a_{10} is a geometri | vedclass

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(B) Given that $a_1, a_2, a_3, \ldots, a_{10}$ is a geometric progression $(GP)$ with first term $a$ and common ratio $r$. We are given $\frac{a_3}{a_

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$5^4$

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(B) Given that $a_1, a_2, a_3, \ldots, a_{10}$ is a geometric progression $(GP)$ with first term $a$ and common ratio $r$. We are given $\frac{a_3}{a_1} = 25$. Since $a_n = ar^{n-1}$,we have $a_3 = ar^2$ and $a_1 = a$. Thus,$\frac{ar^2}{a} = 25$,which implies $r^2 = 25$. We need to find the value of $\frac{a_9}{a_5}$. Using the formula for the $n$-th term,$\frac{a_9}{a_5} = \frac{ar^8}{ar^4} = r^4$. Since $r^2 = 25$,we have $r^4 = (r^2)^2 = (25)^2 = (5^2)^2 = 5^4$.

If $a_1, a_2, a_3, \ldots, a_{10}$ is a geometric progression and $\frac{a_3}{a_1}=25$,then $\frac{a_9}{a_5}$ equals

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