Find the arithmetic series in the question The situation in which the questions are asked are the following: 
When gaining $32$m in depth the temperature gains $1°$C. 
when you are $25$m below the surface temperatures of $10°$ are measured. 
Next they ask two questions : 


*

*At what depth will the temperature be $30°$C

*What temperature will be measured in a mineshaft thats $985$m deep. 


I fail to see the series in this situation can someone help?
 A: An arithmetic series is a synonym for a linear equation, only the naming is more complicated.
The slope of the function $f(x)=ax+b$ must be $\frac{1}{32}$ because $32m$ rise the temperature by $1$ degree.
So, we have $f(x)=\frac{1}{32}x+b$. We also know $f(25)=10$, if we insert this, we get $b=\frac{295}{32}$
So, the temperature is $y=\frac{x+295}{32}$ ($x$ in $m$, $y$ in $°C$). 
Now, question Nr. $2$ should be trivial to answer. For question number $1$, you have to solve the equation $$\frac{x+295}{32}=30$$ for $x$, which should also be not too difficult.
A: You know that at $25$m the temperature is $10°$, so you need to gain $20°$ to reach $30°$, since you gain $1°$ by $32$m, to gain $20°$ you need to add $32 \times 20=640$m. So finally you reach $30°$ at $640+25=665$m.
For the second question, you are $960$m deeper that $25$m, since $960=32 \times 30$, you gained $30°$ relatively to the temperature at $25$m deep, finally at $960$m the temperature is $30+10=40°$. 
If you name $u_n$ the depth at which you reach $n°$, for all $n \geq 10$, you have $u_n=25+(n-10)32$, and you can obtain the same results than below by studying $u_n$. For example : $u_{30}=25+(30-10)32=25+20 \times 32=665$.
For the second question : $u_n=985 \iff 25+(n-10)32=985 \iff 960=(n-10)32 \iff n-10=30 \iff n=40 $
