Identify the correct recursive formula for the following sequence.

Question

2, -2, 2, -2, 2, . . .

(1 point)
Responses

a1=1 and an=an−1−2
a1=1 and an=an−1−2

a1=2 and an=an−1×(−1)
a1=2 and an=an−1×(−1)

a1=0 and an=an−1×(−1)

Answer 1

To identify the correct recursive formula for the given sequence \(2, -2, 2, -2, 2, \ldots\), we need to observe the pattern of the sequence.

1. The first term (\(a_1\)) is 2.
2. The second term (\(a_2\)) is -2.
3. The third term (\(a_3\)) is 2, which is the same as \(a_1\).
4. The fourth term (\(a_4\)) is -2, which is the same as \(a_2\).

From this observation, it's clear that the sequence alternates between 2 and -2. This suggests taking the previous term and multiplying it by -1 to get the next term.

Thus the recursive formula can be expressed as follows:

• Start: \(a_1 = 2\)
• Recursive step: \(a_n = a_{n-1} \times (-1)\) for \(n > 1\)

Therefore, the correct answer is:

a1=2 and an=an−1×(−1)