If the first term of a G.P. a₁, a₂, a₃, ... is unity such that 4 a₂ + 5 a₃ is least, then the common ratio of G.P. is
(a) −2/5
(b) −3/5
(c) 2/5
(d) none of these

Open in App

Solution

(a) − $\frac{2}{5}$

If the first term is 1, then, the G.P. will be $1, r, r^{2}, r^{3}, . . .$

$Now, 5 r^{2} + 4 r = 5 (r^{2} + \frac{4}{5} r) = 5 (r^{2} + \frac{4}{5} r + \frac{4}{25} - \frac{4}{25}) = 5 {(r + \frac{2}{5})}^{2} - \frac{4}{5} This will be the least when r + \frac{2}{5} = 0, i . e . r = - \frac{2}{5} .$

Suggest Corrections

Similar questions

If the first term of a G.P. $a_{1}$ , $a_{2}$ , $a_{3}$ ,.........is unity such that

4 $a_{2}$ + 5 $a_{3}$ is least, then the common ratio of G.P. is

a_{1}, a_{2}, a_{3}, . . . . .

4 a_{2} + 5 a_{3}

If the first of a G.P. $a_{1}, a_{2}, a_{3}, . . . . . . .$ is unity such that $4 a_{2} + 5 a_{3}$ is least, then the common ratio of G.P. is

a_{1}, a_{2}, a_{3}, \dots

4 a_{2} + 5 a_{3}

a_{1}, a_{2}, a_{3}, . .

4 a_{2} + 5 a_{3}

Join BYJU'S Learning Program