Is 49 a triangular number

Answer 1

No.

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The nth triangular number (n must be a whole number > 0) is given by:

tn = 1/2 n(n+1)

Testing for 49:

1/2 n(n+1) = 49

→ n2 + n - 98 = 0

→ n = (-1 ± √393)/2

but 393 is not a square number, so n cannot be a whole number which it must be for a triangular number; thus 49 is not a triangular number.