Question

Find the first four terms of the sequence given the following recursive formula

Formula: an = 2an-1+an-2
Given: a1 = 8, a2 = -3

Answer 1

Using the given recursive formula and initial conditions, the first four terms of the sequence are calculated to be 8, -3, 2, and 1.

Step-by-step explanation:

To find the first four terms of the sequence defined by the recursive formula an = 2an-1 + an-2, we'll use the given initial conditions a1 = 8 and a2 = -3. To find the next term, a3, we apply the formula using n=3:

• a3 = 2a2 + a1
• a3 = 2(-3) + 8
• a3 = -6 + 8
• a3 = 2

Now, for the fourth term, a4, we again apply the formula:

• a4 = 2a3 + a2
• a4 = 2(2) - 3
• a4 = 4 - 3
• a4 = 1

Therefore, the first four terms of the sequence are 8, -3, 2, and 1.