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Home / Multiply both sides by 2: \(n(n+1) = 420\).

Multiply both sides by 2: \(n(n+1) = 420\).

February 22, 2026

$Multiply both sides by 2: \(n(n+1) = 420\).$

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#### \(12x^2 - 10x + 2\)
If the sum of the first \(n\) natural numbers is 210, find \(n\).
Use the formula: \(\frac{n(n+1)}{2} = 210\).
Solve the quadratic equation: \(n^2 + n - 420 = 0\).
Factor: \((n - 20)(n + 21) = 0\).
So \(n = 20\) (since \(n > 0\)).

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