Respuesta :
General Idea:
In an arithmetic sequence, to find the [tex] n^{th} [/tex] term, we need to use the below formula:
[tex] a_n=a_1+(n-1)*d [/tex]
Here [tex] a_n [/tex] gives the [tex] n^{th} [/tex] term
[tex] a_1 [/tex] gives the first term of sequence
d is the common difference and n is the number of terms in the sequence.
Applying the concept:
In our problem it is given that "A company gives each new salesperson a commission of $300 for the sale of a new car",
so [tex] a_1=300 [/tex]
"The salesperson will receive a $100 increase for each addition car the person sells that week"
so[tex] d=100 [/tex]
"find the number of cars a salesperson must sell to earn $4,200 in a week", this means that we need to find the value of n, when [tex] a_n=4200 [/tex]
Setting up the equation based on the arithmetic sequence formula, we get:
[tex] 4200=300+(n-1)*100\\ 4200=300+100n-100\\ 4200=200+100n\\ 100n+200=4200\\ 100n+200-200=4200-200\\ 100n=4000\\ \frac{100n}{100}=\frac{4000}{100} \\ n=40 [/tex]
Conclusion:
New Salesperson has to sell 40 cars to earn $4200 in a week.
