Respuesta :
Answer:
Money earned by selling 175 magazine subscriptions will be 3176.25
Solution:
Given that you are planning to take a summer job selling magazine subscription.
For first subscription, magazine company will help you to pay $0.75
For each additional subscription sold, magazine company will pay you $0.20 more than what was paid for previous subscription.
So for second subscription, payments will be = 0.75 + 0.20 = 0.75 + 0.20 x 1
And for third subscription, payments will be = 0.75 + 0.20 = 0.75 + 0.20 x 2
Generalizing for nth subscription we get
Payments for nth subscription = 0.75 + 0.20(n-1)
so here we can see that arithmetic sequence is formed, having first term
[tex]a_1 = 0.75[/tex] and common difference = d = 0.20
We need to determine sum of above arithmetic sequence for n = 175
Formula for sum of arithmetic sequence is as follows
[tex]\mathrm{S}_{\mathrm{n}}=\frac{n}{2}[2 a+(n-1) d][/tex]
In our case n = 175, a = 0.75, d = 0.20
[tex]\begin{array}{l}{=>\mathrm{S}_{175}=\frac{175}{2}[(2 \times 0.75)+(175-1) 0.20]} \\\\ {=>\mathrm{S}_{175}=\frac{175}{2}[1.5+(174 \times 0.20)]} \\\\ {\Rightarrow \mathrm{S}_{175}=\frac{175}{2} \times 36.3=3176.25}\end{array}[/tex]
Hence money earn by selling 175 magazine subscriptions will be 3176.25
