To find the first six terms of the given sequence, we start with the first term, a1, which is given as 4. The recursive formula for the sequence is an = 2an-1. This means that each term is twice the previous term.
Let’s calculate the terms one by one:
- a1: From the problem, we have a1 = 4.
- a2: Using the formula, a2 = 2 * a1 = 2 * 4 = 8.
- a3: Now, a3 = 2 * a2 = 2 * 8 = 16.
- a4: Next, a4 = 2 * a3 = 2 * 16 = 32.
- a5: Then, a5 = 2 * a4 = 2 * 32 = 64.
- a6: Finally, a6 = 2 * a5 = 2 * 64 = 128.
So, the first six terms of the sequence are:
- a1 = 4
- a2 = 8
- a3 = 16
- a4 = 32
- a5 = 64
- a6 = 128
This simple pattern shows the exponential growth of the sequence, where each term is double the previous one.