Question

if 5,a,b,c,405 are in geometric progression,the find the value of b

Answer 1

From the given sequence,
$b = \sqrt{ac} .....(1)\\ a = \sqrt{5b} ....(2) \\ c = \sqrt{405b} ........(3)$
multiplying (2) and (3)
$ac = \sqrt{5b \times 405b} \\ ac = \sqrt{2025 {b}^{2} } \\ ac = 45b$
from (1),
${b}^{2} = ac \\ therefore \\ {b}^{2} = 45b \\ b = 45$