Pessimist Singularitarian

#2
October 1st, 2016,
22:48
a) We begin with the kinematic equation:

$ \displaystyle s(n)=\frac{a}{2}n^2+un$

And so:

$ \displaystyle \Delta s_n=s(n)-s(n-1)=\frac{a}{2}n^2+un-\frac{a}{2}(n-1)^2-u(n-1)=an+u-\frac{a}{2}$

b) We are given:

$ \displaystyle \Delta s_2=2a+u-\frac{a}{2}=\frac{3}{2}a+u=17$

$ \displaystyle \Delta s_7=7a+u-\frac{a}{2}=\frac{13}{2}a+u=47$

Multiplying both equations by 2, we obtain the 2X2 system:

$ \displaystyle 3a+2u=34$

$ \displaystyle 13a+2u=94$

To proceed, subtract the former equation from the latter, eliminating $u$ and solve the result for $a$. Then use either equation to find $u$ using the value you find for $a$. Once you have $a$ and $u$, you will be able to express $\Delta s_n$ in terms of $n$ alone.