Question

sum of Ist 20 terms of G.P is244 times sum of its Ist 10 terms .common ratio will be??

Answer 1

$$b q + b q ^ {2} + b q ^ {3} + \dots + b q ^ {2 0} = 2 4 4 (b q + \dots + b q ^ {1 0})$$ $$\frac {b \left(1 - q ^ {2 0}\right)}{1 - q} = 2 4 4 \frac {b \left(1 - q ^ {1 0}\right)}{1 - q}$$ $$1 - q ^ {2 0} = 2 4 4 \left(1 - q ^ {1 0}\right)$$ $$x = q ^ {1 0}$$ $$x ^ {2} - 2 4 4 x + 2 4 3 = 0$$ $$(x - 1) (x - 2 4 3) = 0$$ $$x = 1 \Rightarrow q = 1$$ $$x = 2 4 3 \Rightarrow q = \sqrt [ 1 0 ]{3 ^ {5}} = \sqrt {3}$$