If the first term of a G.P. is 5 and the comm | vedclass

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(B) Given that the first term $a = 5$ and the common ratio $r = -5$.Let the $n^{th}$ term be $3125$.The formula for the $n^{th}$ term of a $G.P.$ is $

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$5$

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(B) Given that the first term $a = 5$ and the common ratio $r = -5$.Let the $n^{th}$ term be $3125$.The formula for the $n^{th}$ term of a $G.P.$ is $a_n = a r^{n-1}$.Substituting the given values: $5(-5)^{n-1} = 3125$.Dividing both sides by $5$: $(-5)^{n-1} = 625$.Since $625 = (-5)^4$,we have $(-5)^{n-1} = (-5)^4$.Comparing the exponents,$n - 1 = 4$,which gives $n = 5$.Therefore,the $5^{th}$ term is $3125$.

If the first term of a $G.P.$ is $5$ and the common ratio is $-5$,then which term is $3125$ (in $^{th}$)?

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