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Home / The largest integer \( n \) satisfying this is \( n = 33 \). Verify:

The largest integer \( n \) satisfying this is \( n = 33 \). Verify:

February 22, 2026

$The largest integer \( n \) satisfying this is \( n = 33 \). Verify:$

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Divide by 3:
n - 1 < \frac{98}{3} \approx 32.666\ldots
n < 33.666\ldots
a_{33} = 2 + 32 \cdot 3 = 2 + 96 = 98 < 100
a_{34} = 2 + 33 \cdot 3 = 101 > 100
Thus, there are \(\boxed{33}\) terms before the value exceeds 100.

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