(i) {3,6,9,12}={x:x=3n,nϵN and 1≤n≤4}Alternatively, {x:x is a multiple of 3 and x≤12}
(ii) {2,4,8,16,32}
It can be seen that 2=21,4=22,8=23,16=24, and 32=25.
∴{2,4,8,16,32}={x:x=2n,nϵN and 1≤n≤5}
(iii) {5,25,125,625}
It can be seen that 5=51,25=52,125=53, and 625=54.
∴{5,25,125,625}={x:x=5n,nϵN and 1≤n≤4}
(iv) {2,4,6,....}
It is a set of all even natural numbers.
∴{2,4,6,....}={x:x is an even natural number}
(v) {1,4,9,.....100}
∴{1,4,9...100}={x:x=n2,nϵN and 1≤n≤10}
Alternatively, {x:x is a square of natural number and x≤100}