Let's Think , The Common Difference of this AP Series = d
Now , first term = a
second term = b
So , b = a + d
Or , d = b-a
Now , if there are total ( 2n +1 ) th term in the series , the middle term will be ( n+1) term .
Therefore , c = a + nd = a + n(b-a)
From this we can get , n = (c-a) / (b-a)
So , the total sum = [(2n+1)/2][2a + 2nd ]
You can find out the last term by putting the value of n and d in the above term and rearranging that .