Ans: The sum of an AP is the sum of each term of the AP. The summation of each term of an AP can be tiresome in longer progressions. Also, the APs with a negative common difference, finding the sum of AP can be tricky. The sum of the AP can be calculated using the following formula:S = n/2(2a + (n - 1)d)Derivation: Sn = a1 + (a1 + d) + (a1 + 2d) + .... (a1 + (n - 1)d). (i)Sn = an + (an - d) + (an - 2d) + ...(an - (n - 1)d). (ii)Adding both the equations and solving,2Sn = n(a1 + an)an = a1 + (n - 1)d2Sn = n(a1 + a1 + (n - 1)d)2Sn = n(2a1 + (n - 1)d)S = n/2(2a1 + (n - 1)d)The formula for sum of AP can be written as:S = n/2(2a + (n - 1)d)