The average of the first 7 integers in a seri | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the $13$ consecutive odd integers be $x, x+2, x+4, \dots, x+24$.The average of the first $7$ integers is given as $37$.The first $7$ integers

Vedclass · Accepted Answer

$43$

Vedclass · Answer

(D) Let the $13$ consecutive odd integers be $x, x+2, x+4, \dots, x+24$.The average of the first $7$ integers is given as $37$.The first $7$ integers are $x, x+2, x+4, x+6, x+8, x+10, x+12$.The average of these $7$ integers is the middle term, which is the $4^{	ext{th}}$ term: $x+6 = 37$.Thus, $x = 31$.The entire series consists of $13$ consecutive odd integers starting from $31$: $31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55$.The average of an arithmetic progression is the middle term. For $13$ terms, the middle term is the $\frac{13+1}{2} = 7^{	ext{th}}$ term.The $7^{	ext{th}}$ term is $x + (7-1) 	imes 2 = 31 + 12 = 43$.Alternatively, the $7^{	ext{th}}$ term is $37 + (7-4) 	imes 2 = 37 + 6 = 43$.

The average of the first $7$ integers in a series of $13$ consecutive odd integers is $37$. What is the average of the entire series?

Similar Questions

The average age of $8$ members of a group is $40 \text{ years}$. The age of $1$ member is $55 \text{ years}$. After his retirement,a new member of age $39 \text{ years}$ joins the group. What is the effect of this replacement on the average age of the group?

The average of $17$ numbers is $10.9$. If the average of the first $9$ numbers is $10.5$ and the average of the last $9$ numbers is $11.4$, find the middle number.

The average monthly salary of a staff of $9$ persons is $Rs.\, 2450$. One member of the staff whose monthly salary is $Rs.\, 2650$ is transferred. Find out the average salary of the remaining $8$ persons of the staff (in $Rs.$).

If the average of $x$ and $\frac{1}{x} (x \neq 0)$ is $M$,then the average of $x^{2}$ and $\frac{1}{x^{2}}$ is

An aeroplane travels $2500 \, km$,$1200 \, km$,and $500 \, km$ at $500 \, km/h$,$400 \, km/h$,and $250 \, km/h$ respectively. The average speed is (in $km/h$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module