The sum of the first 20 terms of an arithmetic sequence is p, and the sum of the first 22 is q. Write down expressions for the common difference, and the sum of the first 18 terms.
That is right, The formula for the sum of n terms of an AP is Sn= n/2 [ 2a + ( n-1) d ] Note that it should be 2a and not a.
So there is nothing left for now you have
10 [ 2a+19 d ] = p and 11 [ 2a + 21 d ] = q. now find a the first term and d the common difference and get the result.