If the first term of a G.P. a_1, a_2, a_3, is unity such that 4 a… - Vidyadip

MCQ

If the first term of a G.P. $a_1, a_2, a_3, \ldots$ is unity such that $4 a_2+5 a_3$ is least, then common ratio of G.P. is:

✓
$\frac{-2}{5}$
B
$\frac{-3}{5}$
C
$\frac25$
D
None of these

✓

Answer

Correct option: A.

$\frac{-2}{5}$

$-\frac{2}{5}$

Solution:
If the first term is 1, then, the G.P. will be $1, \text{r},\text{r}^2,\text{r}^3,\ \dots$
Now, $5\text{r}^2+4\text{r}=5\Big(\text{r}^2+\frac45\text{r}\Big)$
$=5\Big(\text{r}^2+\frac45\text{r}+\frac{4}{25}-\frac{4}{25}\Big)$
$=5\Big(\text{r}+\frac25\Big)^2-\frac45$
This will be the least when $\text{r}+\frac25=0,\text{ i.e. }\text{r}=-\frac25.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from SEQUENCES AND SERIES→SEQUENCES AND SERIES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The ratio in which the line joining (3, 4, -7) and (4, 2, 1) is dividing the xy-plane:

The graph of the conic $ x^2 - (y - 1)^2 = 1$ has one tangent line with positive slope that passes through the origin. the point of tangency being $(a, b). $ Then Length of the latus rectum of the conic is

If $–8\leq5\text{x} – 3<7,$ then $\text{x}\in$

A frog is presently located at the origin $(0,0)$ in the $X Y$-plane. It always jumps from a point with integer coordinates to a point with integer coordinates moving a distance of $5$ units in each jump. What is the minimum number of jumps required for the frog to go from $(0,0)$ to $(0,1)$ ?

$\mathop {\lim }\limits_{x \to 0} \frac{{{{(1 + x)}^{1/2}} - {{(1 - x)}^{1/2}}}}{x} = $

The domain of $f(x) = \frac{{{{\log }_2}(x + 3)}}{{{x^2} + 3x + 2}}$ is

${\tan ^2}\theta + {\cot ^2}\theta $ is

What is the equation of the ellipse with foci $( \pm 2,\;0)$ and eccentricity $ = \frac{1}{2}$

Two common tangents to the circle ${x^2} + {y^2} = 2{a^2}$ and parabola ${y^2} = 8ax$ are

The sets Sx are defined to be (x, x + 1, x + 2, x + 3, x + 4) where x = 1, 2, 3,.....80. How many of these sets contain 6 or its multiple?