Final answer:
The explicit formula for the given arithmetic sequence 40, 33, 26, ... is an = 47 - 7n. The pattern is a decrease of 7, making this a sequence with a common difference of -7, and the formula is derived using the arithmetic sequence formula.
Step-by-step explanation:
To write an explicit formula for a sequence, you need to identify the pattern of the sequence first. In the given sequence 40, 33, 26, ..., we can see that the pattern is a decrease of 7 from one term to the next. Therefore, this is an arithmetic sequence with a common difference (d) of -7. To find the explicit formula for the nth term (an), we can use the arithmetic sequence formula an = a1 + (n - 1)d, where a1 is the first term and d is the common difference.
For this sequence, the first term a1 is 40. Plugging the values into the formula gives us an = 40 + (n - 1)(-7). Simplifying this, we get:
an = 40 - 7(n - 1)
an = 40 - 7n + 7
an = 47 - 7n
This is the explicit formula for the given sequence. When using this formula, remember that subscripts that are 1 are not written, as they are understood to imply only one of that particular element or term. Of course, it's important to give me a big explanation part to ensure you understand the reasoning behind these steps.