The ages of the members of a youth club which engages in organising cleanliness campaigns all over the city are in AP 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 .Find the number of members of the club and the age of the eldest member. Plzzzzzzzz please respond AS SOON AS POSSIBLE!

1

Answers

2016-04-01T20:55:25+05:30
Let number of the members be n.
Let the age of the eldest member be Tn.
Sn = 250
d = 3 month i.e. 3/12 years or 1/4 year
a = 7 years

Sn = n/2 (2a+(n-1)d)
250 = n/2 (2(7)+(n-1)1/4)
250 = n/2 (14+1/4 n - 1/4)
250 = 14n/2 + n^2/8 - n/8.......... multiply by 2
500 = 14n + n^2/4 - n/4
500 = (56n + n^2 - n) / 4
2000 = n^2 - 55n
n^2 - 55n - 2000 = 0
n= -18,25
n = 18
 
Tn = a + (n-1)d
= 7 + (25-1)1/4
= 7 + 24/4
= 7 + 6
= 13 
Tn =  13 years
0