MCQ
A sequence $a, a+d, a+2 d, \ldots, a+n d$, has odd number of terms. Find its median.
- A$a+\left(\frac{n-1}{2}\right) d$
- B$a+\left(\frac{n}{2}-1\right) d$
- ✓$a+\left(\frac{n+2}{2}\right) d$
- D$a+\left(\frac{n}{2}+2\right) d$
✓
Answer
Correct option: C.
$a+\left(\frac{n+2}{2}\right) d$
(c) : Clearly, the given sequence is an A.P. with first term $a$ and common difference is $d$. Given, sequence is $a, a+d, a+2 d, a+3 d, \ldots, a+n d$ As, there are odd number of terms, so the median is
$
\left(\frac{n+1+1}{2}\right)^{\text {th }} \text { term }=\left(\frac{n+2}{2}\right)^{\text {th }} \text { term }=a+\left(\frac{n+2}{2}\right) d
$
$
\left(\frac{n+1+1}{2}\right)^{\text {th }} \text { term }=\left(\frac{n+2}{2}\right)^{\text {th }} \text { term }=a+\left(\frac{n+2}{2}\right) d
$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The integral value of $k$ for which the equation $(k-12) x^2+2(k-12) x+2=0$ possesses no real solutions, is
→Which of the following is a quadratic equation?
If $\triangle A B C \sim \triangle D E F, B C=4 \ cm , E F=5 \ cm$ and area of $\triangle A B C=64 \ cm ^2$, find the area of $\triangle D E F$.
→$n^2- 1$ is divisible by $8$, if n is:
→The radius of a wheel is $0.25\ m$. The number of revolutions it will make to travel a distance of $11\ km$ will be:
→The perimeter of a triangle with vertices $A(0,4), O(0,0)$ and $B(3,0)$ is
→In the given figure, a circle is inscribed in a quadrilateral $ABCD$ touching its sides $AB, BC, CD$ and $AD$ at $P, Q, R$ and $S$ respectively. If the radius of the circle is $10cm, BC = 38cm, PB = 27cm$ and $\text{AD} \perp \text{CD}$ then the length of $CD$ is:
→A solid frustum is of height $8\ cm$. If the radii of its lower and upper ends are $3\ cm$ and $9\ cm$ respectively, then its slant height is
→$\pi$ is:
→Common difference $\frac{1}{29}, \frac{1-29}{29}, \frac{1-49}{29}$, is _________
→