Question

Find r if 3r+1,7r,10r+8 are in GP

Answer 1

IF 3 r + 1 , 7 r , 10 r + 8 are in G.P. then -

${(7r)}^{2} = (10r + 8)(3r + 1)$

$49 {r}^{2} = 30 {r}^{2} + 10r + 24r + 8$

$19 {r}^{2} - 34r - 8 = 0$

$r = 2 \: </strong><strong>,</strong><strong> \: r = - \frac{4}{19} ( \times )$