Question

Three number form an increasing g.P. If the middle term is doubled them the new numbers are in



a.P. Find the common ratio of the g.P

Answer 1

Step-by-step explanation:

$\huge\bf{\mid{\overline{\underline{ANSWER}\mid}}} \\ Let \: \: terms \: \: be \implies a, ar, a{r}^{2} \\ \\ According \: \: to \: \: condition..\\ \\ 2(ar) = \frac{a{r}^{2}+ a}{2} \\ \\ a{r}^{2} - 4ar +a = 0 \\ \\ {r}^{2} - 4r +1 = 0 \\ \\ Comparing \: \: with \: \: a{x}^{2} + bx+c = 0 \\ \\ a = 1 ,b = -4,c= 1$ $\\ \\ r = \frac{ -b \pm \sqrt{{b}^{2} - 4ac}}{2a} \\ \\ r = \frac{ 4 \pm \sqrt{12}}{2} \\ \\ r = 2 \pm \sqrt{3} \\ \\ Since, \: \: it \: \: is \: \: increasing \: \: G. P \: \: \\ \\ \huge\boxed{r = 2 + \sqrt{3}}$