Question

write down the first five terms of the following recursively defined sequence.
\\(a_1 = 4\\); \\(a_{n+1} = -2a_n + 2\\)

Explanation:

Step 1: Identify the first term

$$a_1 = 4$$

Step 2: Calculate the second term

$$a_2 = -2a_1 + 2 = -2(4) + 2 = -6$$

Step 3: Calculate the third term

$$a_3 = -2a_2 + 2 = -2(-6) + 2 = 14$$

Step 4: Calculate the fourth term

$$a_4 = -2a_3 + 2 = -2(14) + 2 = -26$$

Step 5: Calculate the fifth term

$$a_5 = -2a_4 + 2 = -2(-26) + 2 = 54$$

Answer:

\(4, -6, 14, -26, 54\)