Chapter 12, Problem 16CT

A weightlifter begins his routine by benching $100$ pounds and increases the weight by $30$ pounds for each set. If he does $10$ repetitions in each set, what is the total weight lifted after $5$ sets?

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To determine

To calculate: The total weight lifted after 5 sets if a weightlifter begins his routine by benching 100 pounds and increases the weight by 30 pounds for each set, if he does 10 repetitions in each set.

Answer to Problem 16CT

Solution:

The weightlifter will have lifted $8000$ pounds after 5 sets.

Explanation of Solution

Given information:

A weightlifter begins his routine by benching 100 pounds and increases the weight by 30 pounds for each set and he does 10 repetitions in each set.

Formula used:

1) For the arithmetic sequence $\left\{a_n\right\}$ whose first term is $a_1$ and common difference is $d$, then the $n^{th}$ term is defined by the formula $a_n=a_1+\left(n-1\right)d$.

2) Sum of the first n terms in the arithmetic sequence is $S_n=\frac{n}{2}(a_1+a_n)$.

Calculation:

Weights from an arithmetic sequence with first term $a_1=100$ and common difference $d=30$.

Suppose weightlifter performs only one repetition per set, the total weight lifted in 5 sets would be the sum of first five terms of the sequence.

$a_1=100$ and need to calculate $a_n$ i.e. $a_5$ here.

$a_n=a_1+\left(n-1\right)d$

$\Rightarrow a_5=100+\left(5-1\right)\cdot 30$

$\Rightarrow a_5=100+4\cdot 30$

$\Rightarrow a_5=220$

Thus sum of the first 5 terms is:

$S_5=\frac{5}{2}\left(100+220\right)=\frac{5}{2}\left(320\right)=800$

Since the weightlifter performs $10$ repetitions in each set, multiply by $10$ to the sum calculated above.

Thus, $10*800=8000$.

Therefore, the weightlifter will have lifted $8000$ pounds after 5 sets.