Chapter 12, Problem 16CT

To determine

To find: The total weight after $5$ set.

Answer to Problem 16CT

The total weight is $8000$ pound.

Explanation of Solution

Given information:

The given, routine is benching $100$ pound and increase weight by $30$ pound per set.

The repetition in each set is $10$ .

Calculation:

Calculate the total weight.

  $\begin{array}{l}=100\times 10+\left(100+30\times 1\right)\times 10+\left(100+30\times 2\right)\times 10+\left(100+30\times 3\right)\times 10+\left(100+30\times 4\right)\times 10\\ =10\times \left[\left(100+30\times 0\right)+\left(100+30\times 1\right)\left(100+30\times 1\right)+\left(100+30\times 1\right)+\left(100+30\times 1\right)\right]\end{array}$

Generalize the solution,

Total weight $\begin{array}{l}={\displaystyle \sum _{n=1}^{5}10\left[100+30\left(n-1\right)\right]}\\ =10{\displaystyle \sum _{n=1}^{5}100+10{\displaystyle \sum _{n=1}^{5}30n}-30}\\ =10\left(100\times 5\right)+10\times 30{\displaystyle \sum _{n=1}^{5}1n+10{\displaystyle \sum _{n=1}^{5}3}0}\\ =10\left(500\right)+300\left[\frac{5\left(5+1\right)}{2}\right]-10\left(30\times 5\right)\\ =5000+300\times 15-1500\\ =8000\end{array}$

Therefore, the total weight is $8000$ pound.