Question

If n is an natural number, then which of the following formula gives the numbers between $n^2$ and $(n+1{)}^2$?

• A. $n-2$
• B. $2n$
• C. $4n$
• D. $n-1$

Answer 1

The correct option is B $2n$

The number of terms between $n^2$ and $(n+1{)}^2$ will be given by:
$t=(n+1{)}^2-n^2-1$
Note that the factor of -1 is used because both of the end numbers are not to be counted.

$t=(n^2+2n+1)-n^2-1$
$t=2n$

We can verify this by an example. For example, if $n=2$:
$(n+1{)}^2=3^2=9$
$n^2=2^2=4$
Terms in between is: {5,6,7,8}
Number of terms is $4=2\times 2$