Math about Geometric series In a geometric series, the sum of $1^{st}$ term $+$ $2^{nd}$ term $+$ $3^{rd}$ term $= 38$, 
the sum of $2^{nd}$ term $+ 4^{th}$ term $=  17 \frac{1}{3}$; 
how to calculate the common ratio? ( it is for sure the answer is $r= \frac{2}{3}$ and the first term $= 18$)

Hint: If your series is geometric with common ratio $r$ and first value $a$... then the terms of the sequence look like $a, ar, ar^{2}, ar^{3},...$.  Write out two equations in those two unknowns ($a$ and $r$) and solve.
The equations come out to be $a+ar+ar^2=38$ and $ar+ar^3=17+1/3$.
