Determine whether sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence.
3, 9, 27, 81
To determine if the given sequence is arithmetic, we need to check if the difference between each consecutive pair of terms is the same.
Taking the difference between consecutive terms:
9 - 3 = 6
27 - 9 = 18
81 - 27 = 54
Since the differences are not the same, the sequence does not appear to be arithmetic.
Therefore, we cannot find the common difference or the next three terms in the sequence.
To determine if the sequence appears to be an arithmetic sequence, we need to check if there is a constant difference between each term.
Let's calculate the differences between consecutive terms:
Second term - First term: 9 - 3 = 6
Third term - Second term: 27 - 9 = 18
Fourth term - Third term: 81 - 27 = 54
From the differences, we can see that there is no constant difference between consecutive terms. Therefore, the sequence does not appear to be an arithmetic sequence.
If the sequence were arithmetic, the common difference would be the same for each term. In this case, there is no common difference.
Since the sequence is not arithmetic, we cannot determine the next three terms.
To determine whether a sequence is an arithmetic sequence, we need to check if there is a common difference between consecutive terms.
Let's compare the difference between consecutive terms:
9 - 3 = 6
27 - 9 = 18
81 - 27 = 54
Since the differences are not constant, the sequence does not appear to be an arithmetic sequence.
To find the common difference and next three terms in a sequence, we need a sequence that follows a specific pattern. In this case, the given sequence seems to follow a different pattern, possibly a geometric sequence where each term is obtained by multiplying the previous term by a constant factor.
To confirm this, let's calculate the ratios between consecutive terms:
9/3 = 3
27/9 = 3
81/27 = 3
The ratios are all equal to 3, indicating a geometric sequence with a common ratio of 3.
To find the common difference, we use the formula:
common difference (d) = common ratio (r) - 1
d = 3 - 1 = 2
The next term in the sequence can be found by multiplying the previous term by the common ratio:
81 * 3 = 243
The next three terms in the sequence would be:
81 * 3 = 243
243 * 3 = 729
729 * 3 = 2187
Therefore, the common difference is 2, and the next three terms in the sequence are 243, 729, and 2187.