Answer:
[tex]a_n=8+7n[/tex]
Step-by-step explanation:
No. of T-Shirts sold in first week = 15
No. of T-Shirts sold in second week = 22
No. of T-Shirts sold in third week = 29
The number of shirts sold each week represents an arithmetic sequence.
15,22,29,....
So, a = first term = 15
d = common difference = 22-15= 29-22= 7
Formula of nth term :[tex]a_n=a+(n-1)d[/tex]
a is the first term
d is the common difference
n is the number of term
Now substitute the values in the formula :
[tex]a_n=15+(n-1)7[/tex]
[tex]a_n=15+7n-7[/tex]
[tex]a_n=8+7n[/tex]
Where n is the number of weeks
Hence the explicit rule for the arithmetic sequence that defines the number of shirts sold in week n is [tex]a_n=8+7n[/tex]
