Question

the ages of members of a youth club which engages in organising cleanliness campaigns all over the coty, are in a A.P. with common difference equal to 3 months.The youngest member is a child of 7 years where as the sum of ages of all members is 250 years. Find the number of members of the club and age of the oldest member!

Answer 1

you have to find in this question the value of 'n' & 'an' . so the answer is 'n' value is 105 & 'an' value is 11 years

Answer 2

The number of members of the club is 25  & age of the oldest member is 13 years.

Step-by-step explanation:

Given:

The ages of youth club  members are in a A.P. with common difference of 3 months.

The age of the  youngest member is a child of 7 years..

The sum of all members  age is 250 years.

To Find:

The number of members of the club  & age of the oldest member.

Formula Used:

Sum of  nth term of the Arithmetic Progression (A.P) Sn =n/2 [2y+(n-1)z]    ----------------------formula no .01

nth term of the Arithmetic Progression (A.P) Tn = y+(n-1)z       ---------------------- formula no.02.

Where

y = the age of the youngest member is a child.

z =  the age common difference.

n =  number of the  members of the club.

Sn= the sum of age   of all members of the club

Tn =  the age of the oldest member

Solution:

As given- The ages of members of a youth club are in a A.P. with common difference of 3 months.

z=3 months = $\frac{3}{12}$ year  $=\frac{1}{4}$ year.

As given- the age of the youngest member is a child of 7 years.

y= 7

As given- The sum of all members  age is 250 years.

Sn=250

Putting values of y,z and Sn in formula no.01.

$Sn=\frac{n}{2} [2y+ (n-1) z]$

$250=\frac{n}{2} [2(7)+ (n-1) (\frac{1}{4} )]$

$500= n [ 14 + (n-1) (\frac{1}{4} )]$

$500= n [ \frac{56+n-1}{4} ]$

$2000= n^{2} + 55n$

$n^{2} +55n-2000=0$

$n^{2} +80n-25n-2000=0$

$n(n+80)-25(n+80)=0$

$(n-25)(n+80)=0$

$n=25, n=80$

Number of people can not be negative.

So, n=25

Number of members of club  is=25

Putting values of y,z and n  in formula no.02.

Age of the oldest member $Tn= 7+(25-1)(\frac{1}{4} )$

                                             $Tn=7+6=13$  years

Thus,the number of members of the club is 25  & age of the oldest member is 13 years.