A={1,4,7,10.......20terms} B={9,16.23,30......20terms} We first need to find n(A∩ B). The nth term of A=1+(n−1)3=3n−2. The mth term of B=9+(m−1)7=7m+2. n(A∩B) will be equal to the number ofsolutions of 3n−2=7m+2 , where n and m are natural numbers not more than 20. ⇒ n=