Download App

STD 11 - 8. sequence and series — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 8. sequence and series1 Mark
MCQ
If $x,\,2x + 2,\,3x + 3,$are in $G.P.$, then the fourth term is
  • A
    $27$
  • B
    $- 27$
  • C
    $13.5$
  • ✓
    $- 13.5$
✓

Answer

Correct option: D.
$- 13.5$
d
(d) Given that $x,\;2x + 2,\;3x + 3$ are in $G.P.$

Therefore, ${(2x + 2)^2} = x(3x + 3) $

$\Rightarrow {x^2} + 5x + 4 = 0$

$ \Rightarrow (x + 4)(x + 1) = 0$

$\Rightarrow x = - 1,\; - 4$

Now first term $a = x$

Second term $ar = 2(x + 1)$

$ \Rightarrow r = \frac{{2(x + 1)}}{x}$

then ${4^{th}}$ term $ = a{r^3}$$ = x{\left[ {\frac{{2(x + 1)}}{x}} \right]^3} = \frac{8}{{{x^2}}}{(x + 1)^3}$

Putting $x = - 4$

We get ${T_4} = \frac{8}{{16}}{( - 3)^3} = - \frac{{27}}{2} = - 13.5$.

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 "M.C.Q (1 Marks)" from STD 11 - 8. sequence and series→STD 11 - 8. sequence and series — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Roots of the equations $2{x^2} - 5x + 1 = 0$, ${x^2} + 5x + 2 = 0$ are
→
The value of the sum $\sum\limits_{n = 1}^{13} {({i^n} + {i^{n + 1}})} $, where $i = \sqrt { - 1} $, equals
→
The domain of definition of $\text{f(x)}=\sqrt{4\text{x}-\text{x}^2}$ is:
→
A quadratic polynomial $ y = f (x)$  with absolute term  $3$  neither touches nor intersects the abscissa axis and is symmetric about the line $x = 1$ . The coefficient of the leading term of the polynomial is unity. A point $A(x_1, y_1)$  with abscissa $x_1 = 1$  and a point $B(x_2, y_2) $ with ordinate $y_2 = 11 $ are given in a cartisian rectangular system of co-ordinates $OXY $ in the first quadrant on the curve $y = f (x)$  where $ 'O'$  is the origin. The scalar product of the vectors $\vec {OA}$ and $\vec {OB}$ is
→
Let ${\left( {1 + x} \right)^{10}} = \sum\limits_{r = 0}^{10} {{C_r}{x^r}} $ and ${\left( {1 + x} \right)^7} = \sum\limits_{r = 0}^7 {{d_r}{x^r}} $ . If $P = \sum\limits_{r = 0}^5 {{C_{2r}}} $ and $Q = \sum\limits_{r = 0}^3 {{d_{2r + 1}}} $ , then $\frac{P}{{2Q}}$ is equal to
→
The equation of the set of point $P,$ the sum of whose distance from $A(4, 0, 0)$ and $B(-4, 0, 0)$ is equal to $10$ is:
→
Let $A_1, A_2, A_3, \ldots \ldots ., A_8$ be the vertices of a regular octagon that lie on a circle of radius $2$ . Let $P$ be a point on the circle and let $\mathrm{PA}_{\mathrm{i}}$ denote the distance between the points $P$ and $\mathrm{A}_{\mathrm{i}}$ for $i=1,2, \ldots, 8$. If $P$ varies over the circle, then the maximum value of the product $\mathrm{PA}_1 \cdot \mathrm{PA}_2 . \cdots \cdot \mathrm{PA}_8$, is
→
$\mathop {\lim }\limits_{x \to \infty } [x({a^{1/x}} - 1)]$,$(a > 1) = $
→
Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. The probability that ${a^2} - {b^2}$ is divisible by $3$ is
→
Eight persons are to be transported from city $A$ to city $B$ in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is $...........$.
→