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Question

Consider that the 1st triangular number is 1, 2nd triangular number is 3, 3rd triangular number is 6 and so on. The 26th triangular number is 351. Determine the 25th triangular number.

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Solution

A nth triangular number is essentially the sum of the first n natural numbers.

1=1
3=1+2
6=1+2+3
.
.
.
and, so on

The 26th triangular number can be written as
1+2+3+..........+24+25+26=351

The sum of the first 25 numbers is the 25th triangular number, so
25th triangular number +26=351

Hence, 25th triangular number =325

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