In the given problem, we need to show that the given sequence is an A.P and then find its common difference.Herean​ = 5n − 7Now, to show that it is an A.P, we will find its few terms by substituting n = 1,2,3,4,5So,Substituting n = 1, we geta1​ = 5(1) − 7a1​ = −2Substituting n = 2, we geta2​ = 5(2) − 7a2​ = 3Substituting n = 3, we geta3​ = 5(3) − 7a3​ = 8Substituting n = 4, we geta4​ = 5(4) − 7a4​ = 13Substituting n = 5, we geta5​ = 5(5) − 7a5​ = 18Further, for the given sequence to be an A.P,We find the common difference (d)a = a2​ − a1​ = a3​ − a2​Thusa2​ − a1​ = 3 − (−2)= 5Alsoa3​ − a2​ = 8 − 3= 5Since a2​ − a1​ = a3​ − a2​Hence, the given sequence is an A.P and its common difference is d = 5