B)

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 ]

= [2*{(c-a)/(b-a)}+1]c

You can find out the last term by putting the value of n and d in the above term and rearranging that .