Question

Find the $312th$ triangular number using the average method.

Answer 1

Step 1: Find the average of $1$ and $312$

the average will be $\frac{312+1}{2}=\frac{313}{2}=156.5$

Step 2: Multiply the average by the largest number

$Average\times Largestnumber=$ $156.5\times 312=48828$

Hence, the $312th$ triangular number is $48828.$