Question

. If (a -- c) is the geometric mean of (a + 2b + c) and (a – 2b + c), show that a, b, c are in
continued proportion.​

Answer 1

Please refer the attachment:)

Answer 2

This gives (a + 2b + c)/(a - c) = (a - c)/(a - 2b + c)

=> (a + 2b + c)(a - 2b + c) = (a - c)^2

=> (a + c)^2 - 4b^2 = (a - c)^2

=> a^2 + c^2 + 2ac - 4b^2 = a^2 + b^2 - 2ac

=> 4ac = 4b^2

=> ac = b^2

=> b/a = c/b

This proves that b is the mean proportion between a and c or b/a = c/b.