Find the $230 t h$ triangular number using the average method.

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Solution

Step 1: Find the average of $1$ and $230$
The average will be $\frac{230 + 1}{2} = \frac{231}{2} = 115.5$
Step 2: Multiply the average by the largest number
$A v e r a g e \times L a r g e s t n u m b e r =$ $115.5 \times 230 = 26565$
Hence, the $230 t h$ triangular number is $26565 .$

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