If the first term of a G.P.

Question:

If the first term of a G.P. a1a2a3, ... 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

Solution:

(a) $-\frac{2}{5}$

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

Now, $5 r^{2}+4 r=5\left(r^{2}+\frac{4}{5} r\right)$

$=5\left(r^{2}+\frac{4}{5} r+\frac{4}{25}-\frac{4}{25}\right)$

$=5\left(r+\frac{2}{5}\right)^{2}-\frac{4}{5}$

This will be the least when $r+\frac{2}{5}=0$, i. e. $r=-\frac{2}{5}$.

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now