An arithmetic series is defined by the expression

$$\sum _{r=8}^{37}(4r-3)$$

(i) Write down the first term of the series. (ii) Write down the common difference of the series. (iii) Find the number of terms of the series.

The energy output of a turbine across various operating frequencies is modeled by a different arithmetic series

$$\sum _{r=20}^{79}(kr+m)$$

where $k$ and $m$ are constants. The total energy output of this series is 10980 units. (i) Show that $49.5k+m=183$. (ii) The 21st term of the series is 15 more than twice the 1st term. Find the values of $k$ and $m$.