sequences: a weightlifter begins his routine by benching 100 pounds

[fellow]

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?

 

[stapel]

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?

What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

 

[fellow]

Confused

I used a+(n-1)d. With a=100, n=5 and d=30, but got another answer because the correct answer was 8000lb when I checked.

 

[JeffM]

I used a+(n-1)d. With a=100, n=5 and d=30, but got another answer because the correct answer was 8000lb when I checked.

Hint.

\(\displaystyle \displaystyle k\left(\sum_{i = 1}^n\{a + d(i - 1)\}\right).\)

Why?

Can you work it out?

 

[soroban]

Hello, fellow!

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

Look at what we have . . .

. . \(\displaystyle \begin{array}{cccc} \text{Set} & \text{Weight} & \text{Reps} & \text{Total} \\ \hline 1 & 100 & 10 & 1000 \\ 2 & 130 & 10 & 1300 \\ 3 & 160 & 10 & 1600 \\ \vdots & \vdots & \vdots & \vdots \\ \hline \end{array}\)


We have an arithmetic series with first term \(\displaystyle a = 1000\),
. . common difference \(\displaystyle d = 300\), and \(\displaystyle n = 5\) terms.

The sum is: .\(\displaystyle S_n \;=\;\frac{n}{2}\big[2a + (n-1)d\big] \)

Therefore: .\(\displaystyle S_5 \;=\;\frac{5}{2}\left[2(1000) + (4)(300)\right]\;=\;8000 \)

 

[HallsofIvy]

Or, since 5 is, after all, a rather small number:
\(\displaystyle \begin{array}{cccc}Set & Weight & Reps & Total \\ 1 & 100 & 10 & 1000 \\ 2 & 130 & 10 & 1300 \\ 3 & 160 & 10 & 1600 \\ 4 & 190 & 10 & 1900 \\ 5 & 220 & 10 & 2200\end{array}\)
so the total is 1000+ 1300+ 1600+ 1900+ 2200= 8000 pounds