Question

a ski club rents cross-country skis. write an explicit formula for the sequence. then graph the sequence
number of days rented 1 2 3 4
rental cost ($) 12 17 22 27
explicit formula: $a_n = square + square n$
a
b

Explanation:

Step1: Identify common difference

The sequence of costs is 12, 17, 22, 27. Calculate the difference between consecutive terms: $17-12=5$, $22-17=5$, $27-22=5$. So the common difference $d=5$, which is the coefficient of $n$.

Step2: Find initial constant term

Use the explicit form $a_n = a_1 + (n-1)d$. Rearrange to $a_n = (a_1 - d) + dn$. Substitute $a_1=12$, $d=5$: $a_1 - d = 12 - 5 = 7$.

Step3: Verify the formula

Check for $n=2$: $a_2=7 + 5(2)=7+10=17$, which matches the table. For $n=3$: $a_3=7+5(3)=22$, which also matches.

Step4: Match the correct graph

The ordered pairs are $(1,12)$, $(2,17)$, $(3,22)$, $(4,27)$. Graph B has points at these coordinates, while Graph A does not.

Answer:

Explicit formula: $a_n = 7 + 5n$
Correct graph: B. (Graph with points at (1,7) is incorrect; the correct graph has points (1,12), (2,17), (3,22), (4,27) which is option B)