Question

What is the next term in the sequence?

1, –3, 9 , –27, . . .

A.
–45


B.
–81


C.
61


D.
81

Answer 1

To find the next term in the sequence \(1, -3, 9, -27, \ldots\), let's examine the pattern:

1. The first term is \(1\).
2. The second term is \(-3\).
3. The third term is \(9\).
4. The fourth term is \(-27\).

We can see that each term alternates in sign and is a multiple of the previous term. Observe:

\[
-3 = 1 \times (-3)
\]
\[
9 = -3 \times (-3) = 3^2 \times -3^{-1}
\]
\[
-27 = 9 \times (-3) = 3^3 \times -3^{-2}
\]

Thus, it seems the sequence is multiplying by \(-3\) each time:

- The first term: \(1\)
- The second term: \(1 \times -3 = -3\)
- The third term: \(-3 \times -3 = 9\)
- The fourth term: \(9 \times -3 = -27\)

Continuing this pattern:

\[
-27 \times -3 = 81
\]

Therefore, the next term in the sequence is \(81\).

So, the correct answer is:

D. 81