Suppose the sequence a_1, a_2, a_3, is a n arithmetic progression… - Vidyadip

MCQ

Suppose the sequence $a_1, a_2, a_3, \ldots$ is a n arithmetic progression of distinct numbers such that the sequence $a_1, a_2, a_4, a_8, \ldots$ is a geometric progression. The common ratio of the geometric progression is

✓
$2$
B
$4$
C
$a_1$
D
not determinable

✓

Answer

Correct option: A.

$2$

a
(a)

We have, $a_1, a_2, a_3, \ldots, a_n$ in an $AP$ and $a_1, a_2, a_4, a_8$ in GP.

Let $a_1=a, a_2=a+d, a _3=a+2 d$ and $a_1$, $a_2, a_4, a_8$ are in $GP$.

Let common ratio is $r$.

$\therefore \quad a_1=a, a_2=a r, a_4=a r^2, a_8=a r^3$

$\therefore a+ d =a r, a+3 d=a r^2, a+7 d=a r^3$

$\Rightarrow \quad 2 d =a r(r-1), 4 d=a r^2(r-1)$

$\Rightarrow \quad r=2$

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 8. sequence and series→8. sequence 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

$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ is integer), if $\theta = $

The sum of $(n - 1)$ terms of $1 + (1 + 3) + $ $(1 + 3 + 5) + .......$ is

By principle of mathematical induction, $2^{4 n-1}$ is divisible by which of the following?

If points $(5, 5)$, $(10, k)$ and $(-5, 1)$ are collinear, then $k =$

Complete 2, 4, 6, 8, _________.

If $\sin A = \frac{4}{5}$ and $\cos B = - \frac{{12}}{{13}},$ where $A$ and $B$ lie in first and third quadrant respectively, then $\cos (A + B) = $

The vertex of the parabola $x^2+8 x+12 y+4=0$ is

Sum of the coefficients in the expansion of $(5 x-4 y)^n$ where $n$ is a positive integer is:

The eccentricity of the ellipse $\frac{\text{x}^2}{\text{b}^2}+\frac{\text{y}^2}{\text{y}^2}=1$ if its latus rectum is equal to one half of its minor axis, is:

In an examination of Mathematics paper, there are $20$ questions of equal marks and the question paper is divided into three sections : $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. A student is required to attempt total $15$ questions taking at least $4$ questions from each section. If section $A$ has $8$questions, section $\mathrm{B}$ has $6$ questions and section $\mathrm{C}$ has $6$ questions, then the total number of ways a student can select $15$ questions is