<PRE><B>Question 725194</B>
If the ages of the students in Class XI are inA.P. with common differnce three months and the age of the youngest student is 16 years . Find the number of students in class XI , if the sum of ages of students in 861 .
---
a(1) = 16 years
d = 3/12 = 1/4
Sum = 861 years
--------------------
a(n) = a(1) + (n-1)d
--------------------------
S(n) = (n/2)(a(1) + a(n)
--------------
861 = (n/2)(16 + 16+(n-1)(1/4))
-------
861 = (n/2)(32 + (n-1)(1/4)
----
861 = 16n + (n^2-n)(1/8)
----
6888 = 128n + n^2-n
---
n^2 + 127n - 6888 = 0
---------------
n = 41
====================
cheers,
Stan H.
======================</PRE>