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
What is the next term in the sequence?
1, –3, 9 , –27, . . .
A.
–45
B.
–81
C.
61
D.
81
1 answer
1 answer