Question

suppose that you plan on taking a summer job selling magazines subscriptions . the magazine company will help you pay $0.75 for selling the first subscription .For each additional subscriptions sold, the magazine company will pay you $0.20 more than what was paid for the previous subscription .How much money will you earn by selling 175 magazine subscriptions ? ​

Answer 1

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

`a_1 = 0.75` 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

`\mathrm{S}_{\mathrm{n}}=(n)/(2)[2 a+(n-1) d]`

In our case n = 175, a = 0.75, d = 0.20

`\begin{array}{l}{=>\mathrm{S}_(175)=(175)/(2)[(2 * 0.75)+(175-1) 0.20]} \\\\ {=>\mathrm{S}_(175)=(175)/(2)[1.5+(174 * 0.20)]} \\\\ {\Rightarrow \mathrm{S}_(175)=(175)/(2) * 36.3=3176.25}\end{array}`

Hence money earn by selling 175 magazine subscriptions will be 3176.25