Question:
What is the sum of the first 20 positive integers?
What is the sum of the first 20 positive integers?
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The sum of the first \( n \) integers can be found using the formula \( \frac{n(n+1)}{2} \).
Updated On: Oct 6, 2025
- 190
- 200
- 210
- 220
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The Correct Option is C
Solution and Explanation
The formula for the sum of the first \( n \) positive integers is:
\[
S_n = \frac{n(n+1)}{2}.
\]
This formula is derived by pairing the first and last terms of the sequence, the second and second-to-last terms, and so on. Each pair sums to \( n+1 \). Since there are \( \frac{n}{2} \) pairs, we multiply by \( n+1 \) and divide by 2.
Now, for \( n = 20 \), we substitute into the formula:
\[
S_{20} = \frac{20(20 + 1)}{2}.
\]
Simplify the expression:
\[
S_{20} = \frac{20 \times 21}{2}.
\]
First, multiply \( 20 \times 21 \):
\[
S_{20} = \frac{420}{2}.
\]
Now, divide by 2:
\[
S_{20} = 210.
\]
Thus, the sum of the first 20 positive integers is:
\[
\boxed{210}.
\]
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