# 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 - Mathematics

MCQ

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

#### Options

• −2/5

• −3/5

• 2/5

•  none of these

#### Solution

− $\frac{2}{5}$ If the first term is 1, then, the G.P. will be$1, r, r^2 , r^3 , . . .$

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

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Q 2 | Page 57