Final answer:
The sequence 1, -6, 36, -216, 1296 is not an arithmetic progression because the differences between consecutive terms are not consistent. Thus, there is no common difference, and it cannot be continued as an arithmetic progression.
Step-by-step explanation:
We need to determine whether the sequence 1, -6, 36, -216, 1296 is an arithmetic progression. An arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a constant, called the common difference, to the previous term. We can find the common difference by subtracting each term from the following term. Let's calculate this for the first two terms:
Common difference (d) = second term - first term
= -6 - 1
= -7
Now, let's check if the same difference applies to the next pairs of terms:
- 36 - (-6) = 42
- -216 - 36 = -252
- 1296 - (-216) = 1512
Since the differences are not the same, the sequence is not an arithmetic progression. Therefore, there is no common difference, and we cannot continue the sequence as if it was an arithmetic progression.
However, we can observe that the absolute value of each term is being multiplied by 6 to obtain the next term. This pattern suggests that the sequence could be a geometric progression instead, where each term is obtained by multiplying the previous term by a constant ratio.