Find the first five terms of the sequence using the recursive rule: a1 = 2/3, and An = 5a N-1

To find the first five terms of the sequence using the recursive rule, we need to apply the rule iteratively to generate each term.

Given the recursive rule: a1 = 2/3 and An = 5a N-1, we can start with a1 and calculate subsequent terms until we find a5.

Step 1: Let's start with a1 = 2/3.

Step 2: To find a2, we substitute N = 2 into the recursive rule (An = 5a N-1):
a2 = 5a1 = 5 * (2/3) = 10/3.

Step 3: To find a3, we substitute N = 3:
a3 = 5a2 = 5 * (10/3) = 50/3.

Step 4: To find a4, we substitute N = 4:
a4 = 5a3 = 5 * (50/3) = 250/3.

Step 5: To find a5, we substitute N = 5:
a5 = 5a4 = 5 * (250/3) = 1250/3.

Therefore, the first five terms of the sequence are:
a1 = 2/3,
a2 = 10/3,
a3 = 50/3,
a4 = 250/3,
a5 = 1250/3.