Find the sum to n terms in the geometric progression $$\sqrt{7}$$, $$\sqrt{21}$$, $$3 \sqrt{7}$$, …

Asked by Abhisek | 1 year ago |  101

##### Solution :-

The given G.P is $$\sqrt{7}$$, $$\sqrt{21}$$, $$3 \sqrt{7}$$, ….

Here,

a = $$\sqrt{7}$$ and

r= $$\dfrac{\sqrt{21}}{\sqrt{7}}=\sqrt{3}$$

$$s_n=\dfrac{a(1-r^n)}{1-r}$$

$$\dfrac{\sqrt{7[1-(\sqrt{3})^n}]}{1-\sqrt{3}}$$

By rationalizing

$$\dfrac{\sqrt{7[1-(\sqrt{3})^n}]}{1-\sqrt{3}}\times\dfrac{1+\sqrt{3}}{1+\sqrt{3}}$$

$$\dfrac{\sqrt{7}(1+\sqrt{3})(1-\sqrt{3})^n)}{1-3}$$

$$\dfrac{\sqrt{7}(1+\sqrt{3})}{2}[(3)^\dfrac{n}{2}-1]$$

Answered by Pragya Singh | 1 year ago

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