Asupermarket finds that the number of boxes of a new cereal sold increases each week. in the first week, only 26 boxes of the cereal were sold. in the next week, 57 boxes of the cereal were sold and in the third week 88 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 = 31n -  5

Step-by-step explanation:

The terms of your sequence are.

26, 57, 88, …

This is an arithmetic sequence, because there is a constant difference of 31 between consecutive terms.

The explicit formula for the nth term of an arithmetic sequence is

aₙ = a₁ + d(n - 1 )

a₁ is the first term, and d is the difference in value between consecutive terms. Thus,  

aₙ = 26 + 31(n - 1) = 26 + 31n - 31

aₙ = 31n - 5

The explicit rule for the arithmetic sequence is aₙ = 31n - 5.

ye

step-by-step explanation:

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.