Question

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 in the previous week.

Answer 1

Answer

Let x_n be number of fruit files at the beginning of week n. Then x_0 = 12, which is the initial condition. And, for every n =1,2,3.... 

x_n = 6 x_(n-1) which is the recurrence relation.

From this, it follows that x_n = 12 * 6^n n =0, 1,2...