Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178.

If the first term of this A.P. is 10, then the median of the A.P. is :

Option 1)
26.5

Option 2)
28

Option 3)
29.5

Option 4)
31

Answers (1)

best_answer

As we learnt in

Sum of n terms of an AP -

$S_{n}= \frac{n}{2}\left [ 2a +\left ( n-1 \right )d\right ]$

and

Sum of n terms of an AP

$S_{n}= \frac{n}{2}\left [ a+l\right ]$

- wherein

$a\rightarrow$ first term

$d\rightarrow$ common difference

$n\rightarrow$ number of terms

Arithmetic mean of n numbers -

$A= \frac{1}{n}\left ( a_{1}+a_{2}+a_{3}- - - - - a_{n} \right )$

- wherein

$a_{1}, a_{2}, a_{3}- - - - - a_{n}$ are the n numbers

Let the AP is $a, a+d, a+2d ...a+\left ( n-4 \right )d, a+\left ( n-3 \right )d, a+\left ( n-2 \right )d, a+\left ( n-1 \right )d$

given $a+a+d+a+2d=39$

$3a+3d=39$

$a+d=13$

$d=13-10$

$d=3\left [ \because a=10 given \right ]$

Now $a+\left ( n-4 \right )d+a+\left ( n-3 \right )d+a+\left ( n-2 \right )d+a\left ( n-1 \right )d$

$\Rightarrow 4a+d\left ( 4n-10 \right )=178$

$\therefore n=14 \left [ put\ a=10 \right ]$

$\left [ d=3 \right ]$

$\therefore$ Series is $10, 13, 16 - - - - -$ upto $14$ terms

$S_{14}=\frac{14}{2}\left [ 2\times 10\dotplus 13\times 3 \right ]=7\left [ 20+39 \right ]$

$\therefore$ mean $= \frac{s_{14}}{14}$

$=\frac{7}{14}\left ( 59 \right )$

$=\frac{59}{2}$

$=29.5$

Option 1)

26.5

Incorrect option

Option 2)

28

Incorrect option

Option 3)

29.5

Correct option

Option 4)

31

Incorrect option

Posted by

Aadil

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 session 2 result date announced; Steps to check NTA session 2 scores

anam-khan

JEE Main 2024 session 2 final answer key soon at jeemain.nta.ac.in; result on April 25

anam-khan

JEE Main 2024 Session 2: Last day to challenge answer key today

Latest Question