Question

On his first day at a Gym, Adrian did $30$ push-ups. On each successive day, he managed to do exactly $3$ more push-ups than on the previous day. After completing his push-ups on the ${30}^{th}$ day, how many push-ups had he completed on all $30$ days?

• A. Fewer than $500$
• B. Between $500$ and $1,000$
• C. Between $1,000$ and $1,500$
• D. Between $1,500$ and $2,000$
• E. More than $2,000$

Answer 1

The correct option is E More than $2,000$

This situation forms an Arithmetic progression where Sum of $n$ terms

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ of which $a_1$ is the first term ; $n$ is the number of terms and $d$ is the difference between the two consecutive terms.
Here, $a_1=30$, $n=30$ and $d=3$
So, $S_{30}=\frac{30}{2}\left[2\right(30)+(30-1\left)3\right]$

$=15\times [60+29(3\left)\right]$

$=15\times 147$

$=2205$
Thus the total number of pushups done in $30$ days is more than $2000$.