Remember that the general explicit rule for arithmetic sequences is f(n) = f(1) + d(n-1).
Explicit rule: f(n) = 4.90 + 4 (n-1) Value of the asked term: f(18) = 72.90 Explanation: See solution.
Practice makes perfect
We need to construct an explicit rule in function notation for the arithmetic sequence represented in the table. Then we will find and interpret the meaning of f(18) in the given context.
Number of battery packs
n
1
2
3
4
Total cost ($)
f(n)
4.90
8.90
12.90
16.90
f(n) represents the total cost, in dollars, of purchasing n battery packs. Since we are dealing with an arithmetic sequence, we can describe it using the general explicit rule.
f(n) = f(1) + d(n-1)
Notice that, in this case, f(1) = 4.90. The next thing we need to do is to find the common difference d. This can be done by finding the difference of any two consecutive terms.
d=f(2)-f(1)=8.90-4.90= 4
We can now substitute the obtained values in the general explicit rule.
f(n) = 4.90 + 4 (n-1)
Finally, to find f(18), we will substitute 18 for n in the above formula.
