<span>One of the main ways that economists measure a nation's standard of living is by looking at their GDP (Gross Domestic Product). Specifically they look at the GDP per capita because it shows how much the country is producing (in dollar figures) per individual. This can show both the wealth and standard of living for a country in an easily comparable form.</span>
If
![d](https://tex.z-dn.net/?f=d)
is the common difference between terms in the sequence
![\{a_n\}](https://tex.z-dn.net/?f=%5C%7Ba_n%5C%7D)
, then
![a_1=-21](https://tex.z-dn.net/?f=a_1%3D-21)
![a_2=a_1+d=-21+d](https://tex.z-dn.net/?f=a_2%3Da_1%2Bd%3D-21%2Bd)
![a_3=a_2+d=-21+2d](https://tex.z-dn.net/?f=a_3%3Da_2%2Bd%3D-21%2B2d)
...
![a_n=a_{n-1}+d=\cdots=-21+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_%7Bn-1%7D%2Bd%3D%5Ccdots%3D-21%2B%28n-1%29d)
You're told that
![S_{16}=-288](https://tex.z-dn.net/?f=S_%7B16%7D%3D-288)
(the sum of the first 16 terms in the sequence, presumably). Well, we know that
![S_{16}=\displaystyle\sum_{n=1}^{16}a_n=\sum_{n=1}^{16}(-21+(n-1)d)](https://tex.z-dn.net/?f=S_%7B16%7D%3D%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5E%7B16%7Da_n%3D%5Csum_%7Bn%3D1%7D%5E%7B16%7D%28-21%2B%28n-1%29d%29)
![S_{16}=\displaystyle(-21-d)\sum_{n=1}^{16}1+d\sum_{n=1}^{16}n](https://tex.z-dn.net/?f=S_%7B16%7D%3D%5Cdisplaystyle%28-21-d%29%5Csum_%7Bn%3D1%7D%5E%7B16%7D1%2Bd%5Csum_%7Bn%3D1%7D%5E%7B16%7Dn)
Recall that
![\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5Ekn%3D%5Cfrac%7Bk%28k%2B1%29%7D2)
so that we have
![-288=16(-21-d)+\dfrac{16(16+1)}2d\implies d=\dfrac25](https://tex.z-dn.net/?f=-288%3D16%28-21-d%29%2B%5Cdfrac%7B16%2816%2B1%29%7D2d%5Cimplies%20d%3D%5Cdfrac25)
So we get
Answer:
ÑÑÑÑÑÑÑÑÑÑ ÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑ ÑÑÑÑÑÑÑÑÑÑ
Three points define a triangle.