Find a recurrence relation and initial condition for the num

Find a recurrence relation and initial condition for the number of fruit flies in a jar if there are 12 flies initially and every week there are six times as many flies in the jar as there were the previous week.

Solution

a_0=12, initial condition ie initial number of flies

where,a_n gives number of flies after n weeks

And every week we have 6 times as many flies

a_n=a_{n-1},n>0 , recurrence relation