Question

A sequence is defined by $a_n=\frac{n^2-1}{n+1}$. The difference of its 1000th and 900th term is

• A. 100
• B. 200
• C. 300
• D. 1

Answer 1

The correct option is A 100

$a_n=\frac{n^2-1}{n+1}=\frac{\left(n+1\right)\left(n-1\right)}{n+1}=n-1a_{1000}-a_{900}=\left(1000-1\right)-\left(900-1\right)=100$