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Mathematics

Find the sum of first n terms of the G.P. 5,15,45\sqrt{5}, \sqrt{15}, \sqrt{45}, ………..

AP GP

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Answer

Common ratio (r) = 155=5×35=3\dfrac{\sqrt{15}}{\sqrt{5}} = \dfrac{\sqrt{5} \times \sqrt{3}}{\sqrt{5}} = \sqrt{3}.

By formula,

Sum of first n terms of G.P. = a(rn−1)(r−1)\dfrac{a(r^n - 1)}{(r - 1)}

Substituting values we get :

(S)=5[(3)n−1]3−1(S) = \dfrac{\sqrt{5}[(\sqrt{3})^n - 1]}{\sqrt{3} - 1}.

Hence, sum of first n terms of the G.P. 5,15,45..... is 5[(3)n−1]3−1.\sqrt{5}, \sqrt{15}, \sqrt{45} ….. \text{ is } \dfrac{\sqrt{5}[(\sqrt{3})^n - 1]}{\sqrt{3} - 1}.

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