Find the sum of the first 20 terms of the arithmetic series if a1=4 and a20=62.

To find the sum of the first 20 terms of an arithmetic series, you can use the formula:

\[
S_n = \frac{n}{2} \cdot (a_1 + a_n)
\]

where:
- \(S_n\) is the sum of the first \(n\) terms,
- \(n\) is the number of terms,
- \(a_1\) is the first term,
- \(a_n\) is the \(n\)th term (in this case, the 20th term).

Given:
- \(a_1 = 4\)
- \(a_{20} = 62\)
- \(n = 20\)

Substituting the values into the formula:

\[
S_{20} = \frac{20}{2} \cdot (4 + 62) = 10 \cdot 66 = 660
\]

### Answer:
The sum of the first 20 terms of the arithmetic series is \(660\).

Would you like any further details or have any questions?

Here are 8 related questions you might consider:
1. How do you derive the sum formula for an arithmetic series?
2. What is the sum of the first 50 terms if \(a_1 = 3\) and \(a_{50} = 150\)?
3. How would you find the common difference if the first and last terms are known?
4. Can you find the sum of the first 100 terms of an arithmetic series with \(a_1 = 5\) and \(d = 3\)?
5. How does the sum of an arithmetic series change as the common difference changes?
6. How would you find the sum if only the first term and common difference are known?
7. What is the sum of the first 15 terms of an arithmetic series where \(a_1 = 7\) and \(a_{15} = 49\)?
8. How would you find the sum of the first \(n\) terms if the common difference is negative?

**Tip:** In arithmetic series problems, knowing either the first and last term or the first term and the common difference simplifies finding the sum.

Learn how to calculate the sum of the first 20 terms of an arithmetic series where the first term a1=4 and the 20th term a20=62. Understand the formula for the sum of an arithmetic series and apply it to find the solution. Suitable for high school students studying arithmetic sequences and series.

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