Question

Without drawing a diagram, find
$\left(i\right)10\text{th}$ square number
$\left(ii\right)6\text{th}$ triangular number.

Answer 1

$\left(i\right)10\text{th}$ square number

$n\text{th}$ square number: A square number can easily be remembered by the following rule:
$n\text{th}$ square number $=n^2$
$\Rightarrow$ $10\text{th}$ square number $={10}^2=100$
$\left(ii\right)6\text{th}$ triangular number.

$n\text{th}$ triangular number: A triangular number can easily be remembered by the following rule:

$n\text{th}$triangular number $=\frac{n(n+1)}{2}$
$\Rightarrow$ $6\text{th}$ triangular number

$=\frac{6(6+1)}{2}$

$=\frac{6\times 7}{2}$

$=3\times 7$

$=21$

$\Rightarrow$ $6\text{th}$ triangular number is $21$.