The first term of a G.P. is 7,the last term i | vedclass

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(D) Given: First term $a = 7$,last term $l = a r^{n-1} = 448$,and sum of $n$ terms $S_n = 889$.The formula for the sum of $n$ terms of a $G.P.$ is $S_

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$2$

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(D) Given: First term $a = 7$,last term $l = a r^{n-1} = 448$,and sum of $n$ terms $S_n = 889$.The formula for the sum of $n$ terms of a $G.P.$ is $S_n = \frac{a(r^n - 1)}{r - 1}$.We can rewrite this as $S_n = \frac{a r^n - a}{r - 1} = \frac{(a r^{n-1})r - a}{r - 1}$.Substituting the given values: $889 = \frac{448r - 7}{r - 1}$.Multiplying both sides by $(r - 1)$: $889(r - 1) = 448r - 7$.$889r - 889 = 448r - 7$.$889r - 448r = 889 - 7$.$441r = 882$.$r = \frac{882}{441} = 2$.Therefore,the common ratio is $2$.

The first term of a $G.P.$ is $7$,the last term is $448$,and the sum of all terms is $889$. Then the common ratio is:

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