Question

A club consistes of members whose ages re AP, the common difference being is 3 months. If the youngest member of the club is just 7 years old and the sum of the the ages of all the members is 250 years, then the number of members in the club are

Answer 1

a=7yrs, d=3/12=1/4yrs, Sn=250
Sn=n/2[2a+(n-1)d]
250 =n/2[14+(n-1)1/4]
250=n[14-1/4n-1/4]
500=1/4n²+55/4n
2000=n²+55n
n²+55n-2000=0
n²+80n-25n-2000=0
n(n+80)-25(n+80)=0
(n-25)(n+80)=0
n=25,n=-80(neglected)
n=25