Answer: the values of each prize are
$330,$300,$270,$240,$210,$180,$150.
<h3>
Given: </h3>
- sum of total prize money=$1680
- number of students=7
- each prize is $30 less than the preceding prize
The above conditions are in the form of an Arithmetic Progression(AP)
with sum of series(
) 1680 , 7 terms(n) in the AP and common ratio(d)=30
Let the first term of the AP be 'a'.
![S_{n}=\frac{n}{2}[2a+(n-1)*d]](https://tex.z-dn.net/?f=S_%7Bn%7D%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29%2Ad%5D)
![1680=\frac{7}{2}[2a+(7-1)*30] \\1680=\frac{7}{2} [2a+180]\\1680*2=7*(2a+180)\\3360=14a+1260\\14a=3360-1260\\14a=2100\\a=2100/14\\a=150](https://tex.z-dn.net/?f=1680%3D%5Cfrac%7B7%7D%7B2%7D%5B2a%2B%287-1%29%2A30%5D%20%5C%5C1680%3D%5Cfrac%7B7%7D%7B2%7D%20%5B2a%2B180%5D%5C%5C1680%2A2%3D7%2A%282a%2B180%29%5C%5C3360%3D14a%2B1260%5C%5C14a%3D3360-1260%5C%5C14a%3D2100%5C%5Ca%3D2100%2F14%5C%5Ca%3D150)
The 7th award is $150
The 6th award is $(150+30)=$180
The 5th award is $(180+30)=$210
The 4th award is $(210+30)=$240
The 3rd award is $(240+30)=$270
The 2nd award is $(270+30)=$300
The 1st award is $(300+30)=$330
Reference: To know more about Arithmetic Progressions :
brainly.com/question/13989292
//SPJ2