Question

7 th term of the sequence √2,√10,5√2,..... is

Answer 1

given series is GP so first find first term and common ratio

Answer 2

$a = \sqrt{2} \\ \\ r = \frac{\sqrt{10}}{\sqrt{2}} = \sqrt{\frac{10}{2}} = \sqrt{5} \\ \\ \\ T_7 = ar^6 \\ \\ = \sqrt{2} \times (\sqrt{5})^6 \\ \\ = \sqrt{2} \times (\sqrt{5})^{2 \times 3} \\ \\ = \sqrt{2} \times ((\sqrt{5})^2)^3 \\ \\ = \sqrt{2} \times 5^3 \\ \\ = \sqrt{2} \times 125 \\ \\ = 125\sqrt{2}$