<u>Answer:</u>
Money earned by selling 175 magazine subscriptions will be 3176.25
<u>Solution:
</u>
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
and common difference = d = 0.20
We need to determine sum of above arithmetic sequence for n = 175
<u><em>Formula for sum of arithmetic sequence is as follows
</em></u>
![\mathrm{S}_{\mathrm{n}}=\frac{n}{2}[2 a+(n-1) d]](https://tex.z-dn.net/?f=%5Cmathrm%7BS%7D_%7B%5Cmathrm%7Bn%7D%7D%3D%5Cfrac%7Bn%7D%7B2%7D%5B2%20a%2B%28n-1%29%20d%5D)
In our case n = 175, a = 0.75, d = 0.20
![\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}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%3D%3E%5Cmathrm%7BS%7D_%7B175%7D%3D%5Cfrac%7B175%7D%7B2%7D%5B%282%20%5Ctimes%200.75%29%2B%28175-1%29%200.20%5D%7D%20%5C%5C%5C%5C%20%7B%3D%3E%5Cmathrm%7BS%7D_%7B175%7D%3D%5Cfrac%7B175%7D%7B2%7D%5B1.5%2B%28174%20%5Ctimes%200.20%29%5D%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20%5Cmathrm%7BS%7D_%7B175%7D%3D%5Cfrac%7B175%7D%7B2%7D%20%5Ctimes%2036.3%3D3176.25%7D%5Cend%7Barray%7D)
Hence money earn by selling 175 magazine subscriptions will be 3176.25