Question

If k,2(k+1),3(k+1) are in GP then k=_______

Answer 1

Step-by-step explanation:

k, 2(k+1), 3(k+1) →→ k, 2k + 2, 3k + 3

In a GP, the common ration is,

$\frac{t2}{t1} = \frac{t3}{t2}$

$\frac{2k + 2}{k} = \frac{3(k + 1)}{2(k + 1)}$

$\frac{2k}{k} + \frac{2}{k} = \frac{3}{2}$

$2 + \frac{2}{k} = \frac{3}{2}$

$\frac{2}{k} = \frac{3}{2} - 2$

$\frac{2}{k} = \frac{ - 1}{2}$

$k = - 4$