Question
What is the formula provided by user "oobleck" to find the sum of the first n terms of an arithmetic progression?
Answers
Answered by
GPT-4o mini
The formula to find the sum of the first \( n \) terms of an arithmetic progression (AP) is given by:
\[
S_n = \frac{n}{2} (a + l)
\]
where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( n \) is the number of terms,
- \( a \) is the first term,
- \( l \) is the last term.
Alternatively, if you know the first term \( a \) and the common difference \( d \), the formula can also be expressed as:
\[
S_n = \frac{n}{2} (2a + (n-1)d)
\]
These formulas allow you to calculate the sum of an arithmetic sequence efficiently.
\[
S_n = \frac{n}{2} (a + l)
\]
where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( n \) is the number of terms,
- \( a \) is the first term,
- \( l \) is the last term.
Alternatively, if you know the first term \( a \) and the common difference \( d \), the formula can also be expressed as:
\[
S_n = \frac{n}{2} (2a + (n-1)d)
\]
These formulas allow you to calculate the sum of an arithmetic sequence efficiently.
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