b Even if the sequence is not arithmetic, can the future values be estimated?
A
aDoes the Graph Represent an Arithmetic Sequence? No Explanation: See solution.
B
b See solution.
Practice makes perfect
a From the graph we can estimate the approximate costs. Let's write a sequence whose terms are costs of the advertisements.
20 000, 32 000, 45 000, 57 500
To determine whether this sequence is arithmetic, we will find the differences between consecutive terms.
We see that the difference between consecutive terms is notconstant. Therefore, there is not a common difference. This means that the graph does not represent an arithmetic sequence.
b Let's assume that the increase in cost will be, on average, $12 500. Therefore, to find the cost of a six-page advertisement in the magazine, we need to find the sixth term of our sequence. We already know that the fourth term is 57 500. This means that we have to add 12 500 to this number twice.
57 500 + 12 500 ⟶70 000+ 12 500 ⟶82 500
The sixth term of this sequence is 82 500. Therefore, we can estimate that the cost of a six-page advertisement in the magazine would be about $82 500.
