Question

a club consists of members whose ages are in AP the common difference being 4 months if the youngest member of the club is 88 year old and the sum of Ages of all the members is 168 find the total number of members in the club​

Answer 1

Given:-

• Common difference = 4 months
• a1 (younget memberof the club) = 88 years old
• Sum of ages of the member is 168

Find:-

Number of members in the club.

Solution:-

Sn = n/2 [2a + (n - 1)d]

We have..

a1 = 88 × 12 = 1056

d = 4

Sn = 168 × 12 = 2016

Substitute these values in above formula

=> 2016 = n/2 [2(1056) + (n - 1)4]

=> 2016(2) = n(2112 + 4n - 4)

=> 4032 = n(2108 + 4n)

=> 4032 = 2108n + 4n²

=> 4n² + 2108n - 4032 = 0

=> n² + 527n - 1008 = 0

Using quadratic formula:

=> n = $\sf\frac{ - b \pm \sqrt{( {b)}^{2} -4ac } }{2a}$

=> $\sf\frac{ - 527 \pm \sqrt{( {527)}^{2} -4(1)( - 1008) } }{2(1)}$

=> $\sf\frac{ - 527 \pm \sqrt{277729 \: + \: 4032} }{2}$

=> $\sf\frac{ - 527 \pm \sqrt{281761 } }{2}$

=> $\sf\frac{ - 527 + 531 }{2}$

=> $\sf\frac{ 4 }{2}$

=> $\sf{2}$

Similarly,

=> $\sf\frac{ - 527 - 531 }{2}$

=> $\sf\frac{ - 1058 }{2}$

(Members can't be negative so, negative one is neglected)

•°• Number of members in the club is 2.