Let's call the first term of the sequence "a" and the common difference "d".
The formula for the sum of the first n terms of an arithmetic sequence is: Sn = n/2(2a + (n-1)d).
Using this formula, we can find the value of d:
For the first eight terms:
8/2(2a + (8-1)d) = 60
Solving for d:
d = (60 - 2a) / 14
For the next six terms:
6/2(2a + (9-1)d) = 108
Solving for a:
a = (108 - 6d) / 10
Now that we have the values of a and d, we can find the 25th term using the formula for the nth term of an arithmetic sequence: an = a + (n-1)d.
an = a + (25-1)d = a + 24d
Plugging in the values of a and d found above, we get the 25th term:
an = (108 - 6d) / 10 + 24 [(60 - 2a) / 14] = (108 - 6d) / 10 + 24 [(60 - 2(108 - 6d) / 10) / 14]
Simplifying further, we can find the 25th term