If a, ;b, ;c, ;d, ;e, ;f are in A.P., then the value of e - c wil… - Vidyadip

MCQ

If $a,\;b,\;c,\;d,\;e,\;f$ are in $A.P.$, then the value of $e - c$ will be

A
$2(c - a)$
B
$2(f - d)$
✓
$2(d - c)$
D
$d - c$

✓

Answer

Correct option: C.

$2(d - c)$

c
(c) $a,\;b,\;c,\;d,\;e,\;f$ are in $A.P.$

So $b - a = c - b = d - c = e - d = f - e = K$

Where $K$ is a common difference.

Now, $d - c = e - d$

$ \Rightarrow $$e + c = 2d$.

$e{\rm{-}}c + {\rm{2}}c = 2d $

$\Rightarrow e - c = 2(d - c)$.

Trick : Check by putting $a = 1,\;b = 2,\;c = 3,\;d = 4,\;e = 5$ and $f = 6$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let the function $f(x)=\left\{\begin{array}{cc}\frac{\log _{e}(1+5 x)-\log _{e}(1+\alpha x)}{x} & \text { if } x \neq 0 \\ 10 & \text {; if } x=0\end{array}\right.$ be continuous at $x=0$.The $\alpha$ is equal to.

If $\frac{1}{{{1^4}}} + \frac{1}{{{2^4}}} + \frac{1}{{{3^4}}} + ..... + \infty = \frac{{{\pi ^4}}}{{90}}$, then the value of $\frac{1}{{{1^4}}} + \frac{1}{{{3^4}}} + \frac{1}{{{5^4}}} + .....\infty $ is

Let $k_1$, $k_2$ be the maximum and minimum values of $k$ for which the system of equations given by

$x + ky = 1$ ; $kx + y = 2$; $x + y = k$ are consistent then $k_1^2 + k_2^2$ is equal to

A dice is thrown $5$ times, then the probability that an even number will come up exactly $3$ times is

If the roots of the equation ${x^2} + 2mx + {m^2} - 2m + 6 = 0$ are same, then the value of $m$ will be

The equation of a line passing through the centre of a rectangular hyperbola is $x -y -1 = 0$. If one of the asymptotes is $3x -4y -6 = 0$, the equation of other asymptote is

If $a$ is perpendicular to $b$ and $c,|a| = 2,|b| = 3$, $|c| = 4$ and the angle between $b$ and $c$ is $\frac{{2\pi }}{3}$, then $[a\;b\;c]$ is equal to

Find definite integral of $\int_a^b {\frac{1}{x}dx} $

A ray of light through $(2,1)$ is reflected at a point $P$ on the $y$ - axis and then passes through the point $(5,3)$. If this reflected ray is the directrix of an ellipse with eccentrieity $\frac{1}{3}$ and the distance of the nearer focus from this directrix is $\frac{8}{\sqrt{53}}$, then the equation of the other directrix can be :

If the system of linear equation $x + 2ay + az = 0,$ $x + 3by + bz = 0,$ $x + 4cy + cz = 0$ has a non zero solution, then $a,b,c$