A supermarket finds that the number of boxes of a new cereal sold increases each week. In the first week, only 16 boxes of the cereal were sold. In the next week, 33 boxes of the cereal were sold and in the third week 50 boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
What is the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n?
an=17n+1
an=17n−1
an=17n+33 <my choice
an=17n−33
actually.. im rethinking it out i feel like it might be B
and we have a winner! B it is
The explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n is:
an = 17n + 33
To find the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n, we can first identify the common difference (d) between consecutive terms.
From the information given, we can observe that the number of boxes sold increases by 17 each week. In the first week, 16 boxes were sold, and in the second week, 16 + 17 = 33 boxes were sold. Similarly, in the third week, 33 + 17 = 50 boxes were sold.
Since the common difference is 17, we can now proceed to find the explicit rule for the arithmetic sequence. The explicit rule can be written in the form:
an = a + (n - 1) * d
Where "an" represents the nth term of the sequence, "a" is the first term, "n" is the term number, and "d" is the common difference.
In this case, the first term (a) is 16, and the common difference (d) is 17. Plugging in these values, we get:
an = 16 + (n - 1) * 17
Simplifying further:
an = 16 + 17n - 17
an = 17n - 1
Therefore, the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n is:
an = 17n - 1