The Correct Answer and Explanation is:
The eighth term in this pattern is 21.
To find the eighth term in the sequence 7, 12, 10, 15, 13, …, we must first identify the underlying rule that governs the progression of the numbers. This is not a simple arithmetic sequence, where a constant number is added or subtracted, nor is it a geometric sequence where a constant number is multiplied or divided. Instead, it follows a more complex, alternating pattern.
Let’s examine the operations between each consecutive term. To get from the first term, 7, to the second term, 12, we add 5 (7 + 5 = 12). To get from the second term, 12, to the third term, 10, we subtract 2 (12 – 2 = 10). To get from the third term, 10, to the fourth term, 15, we again add 5 (10 + 5 = 15). Finally, to get from the fourth term, 15, to the fifth term, 13, we again subtract 2 (15 – 2 = 13).
This reveals a consistent, repeating rule: the pattern alternates between adding 5 to one term and then subtracting 2 from the next. We can use this established rule to continue the sequence and determine the subsequent terms until we reach the eighth position.
We are given the first five terms: 7, 12, 10, 15, 13. The last operation performed was subtracting 2. Therefore, to find the sixth term, we must apply the next operation in the pattern, which is adding 5.
- Sixth term: 13 + 5 = 18
Now, we apply the next operation, subtracting 2, to find the seventh term.
- Seventh term: 18 – 2 = 16
To find the eighth and final term for this problem, we apply the next operation in the sequence, which is adding 5.
- Eighth term: 16 + 5 = 21
Therefore, by methodically applying the alternating pattern of adding 5 and subtracting 2, we can confidently determine that the eighth term in this number pattern is 21.
