The 14th term of an A.P is 96,while 25th term is 173 find the ,19th term,sum of 13th and 56th terms,product of 6th and 13th terms.
You are just using the standard definitions here:
14th term --> a + 13d = 96
25th term --> a + 24d = 173
subtract them:
11d = 77
d = 7
back in a + 13d = 96
a + 91 = 96
a = 5
Now you can find any term, e.g.
19th term = a + 18d
= 5 + 18(7) = 131
once you have the terms involved just do the operations asked for
Sn=n/2(2a+(n-1)d)
S56=56/2(2x5+(56-1)x7)
......=28(10+55x7)
...... =28(395)
........ =11060
S56=11060