Sequences with pattern: ACT Math Practice Question

Try this ACT math practice question that tests your ability to recognize a pattern in sequence questions.

In the sequence $s_1$, $s_2$, $s_3$, $\ldots$, the $n$th term of the sequence is given by $s_{n}=\dfrac{n}{n+1}$ for all positive integers $n$. For example, when $n=1$, $s_1 = \dfrac{1}{2}$. What is the product of the first $100$ terms of this sequence?

1. $\quad \displaystyle \frac{1}{100}$
2. $\quad \displaystyle \frac{1}{101}$
3. $\quad \displaystyle \frac{99}{100}$
4. $\quad \displaystyle \frac{100}{101}$
5. $\quad \displaystyle \frac{101}{100}$

Choice B

Video explanation