Answer:
To find the nth term in the sequence 7, 14, 27, 46, 71, we need to examine the pattern and understand how each term relates to the position in the sequence.
Let's analyze the differences between consecutive terms:
- The difference between the 2nd and 1st terms is 14 - 7 = 7.
- The difference between the 3rd and 2nd terms is 27 - 14 = 13.
- The difference between the 4th and 3rd terms is 46 - 27 = 19.
- The difference between the 5th and 4th terms is 71 - 46 = 25.
As you can see, the differences between consecutive terms are not constant. Therefore, the sequence does not have a common difference, which means it is not an arithmetic sequence.
However, we can observe that the differences between consecutive terms are increasing by 6 each time. To find the nth term, we can use this information to determine a formula.
Let's consider the differences again:
- The difference between the 2nd and 1st terms is 7.
- The difference between the 3rd and 2nd terms is 7 + 6 = 13.
- The difference between the 4th and 3rd terms is 13 + 6 = 19.
- The difference between the 5th and 4th terms is 19 + 6 = 25.
From this pattern, we can deduce that the nth term in the sequence can be found by adding the previous term's difference (starting with 7) to the previous term.
For example:
- The 2nd term is 7 + 7 = 14.
- The 3rd term is 14 + 13 = 27.
- The 4th term is 27 + 19 = 46.
- The 5th term is 46 + 25 = 71.
Therefore, the formula for finding the nth term is:
- The nth term = (n - 1)th term + (n - 1)th term's difference.
- In this case, the nth term = (n - 1)th term + (7 + (n - 2) * 6).
For example:
- The 1st term is 7.
- The 2nd term is 7 + (7 + (2 - 2) * 6) = 14.
- The 3rd term is 14 + (7 + (3 - 2) * 6) = 27.
- The 4th term is 27 + (7 + (4 - 2) * 6) = 46.
- The 5th term is 46 + (7 + (5 - 2) * 6) = 71.
Using this formula, you can find the nth term for any position in the sequence.