Question

if a b and c are in gp then a-b/b-c is equal to

Answer 1

$\dfrac{a - b}{b - c} = \dfrac{1}{r}$ where, r is the common ratio.

Step-by-step explanation:

Given that a, b, c are in G.P. Therefore, if the common ratio of the G.P. is r, then b = ar and c = ar².

Now, we are asked to determine the value of $\frac{a - b}{b - c}$.

So, $\frac{a - b}{b - c} = \frac{a - ar}{ar - ar^{2}} = \frac{a(1 - r)}{ar(1 - r)} = \frac{a}{ar} = \frac{1}{r}$ {Since, r can not be 1, hence (r - 1) ≠ 0, and a ≠ 0} (Answer)