find the sum of the first 20th terms of the arithmetic sequence 102 110 118 126

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

\[
S_n = \frac{n}{2} \times \left(2a + (n-1) \times d\right)
\]

Where:
- \( S_n \) is the sum of the first \( n \) terms.
- \( n \) is the number of terms.
- \( a \) is the first term.
- \( d \) is the common difference.

Given:
- \( a = 102 \)
- \( d = 110 - 102 = 8 \)
- \( n = 20 \)

Substitute the values into the formula:

\[
S_{20} = \frac{20}{2} \times \left(2 \times 102 + (20-1) \times 8\right)
\]

\[
S_{20} = 10 \times \left(204 + 19 \times 8\right)
\]

\[
S_{20} = 10 \times \left(204 + 152\right)
\]

\[
S_{20} = 10 \times 356 = 3560
\]

So, the sum of the first 20 terms of the arithmetic sequence is **3560**.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:
1. How would you find the sum of the first 30 terms of the same sequence?
2. What is the 50th term of this arithmetic sequence?
3. How would the sum change if the common difference were 12 instead of 8?
4. Can you derive the formula for the sum of an arithmetic sequence from scratch?
5. How would you find the sum of the first 20 even terms in the sequence?

**Tip:** Always double-check the common difference when working with arithmetic sequences to ensure accurate calculations.

Learn how to find the sum of the first 20 terms of the arithmetic sequence 102, 110, 118, 126 using the formula for the sum of an arithmetic sequence. Detailed step-by-step solution provided. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation