What is the largest integer $n$ for which $1 + 2 + 3 + \dots + n < 500$ ?

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More Arithmetic and geometric sequences questions

An arithmetic sequence has third term $11$ and seventh term $27$ . What is the $20$ th term?
What is the sum of the first $20$ terms of the arithmetic sequence $3, 7, 11, \dots$ ?
A geometric sequence has first term $5$ and common ratio $2$ . What is the sum of its first $8$ terms?
The geometric series $8 + 4 + 2 + 1 + \dots$ continues indefinitely. What is its sum to infinity?
A geometric sequence of positive terms has second term $6$ and fourth term $54$ . What is the first term?
What is the value of $3 + 5 + 7 + \dots + 21$ ?

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