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los primeros cinco terminos de la sucesion

The problem asks for the calculation of the sum of the numbers \(5, 8, 11, 14, 17\) using the sequence \(5, 8, 11, 14, 17, 20, 23, \dots\).

This sequence is an arithmetic sequence where:
- The first term \(a_1 = 5\)
- The common difference \(d = 3\) (since \(8 - 5 = 3\), \(11 - 8 = 3\), etc.)

To find the sum of the first five terms, you can use the formula for the sum \(S_n\) of the first \(n\) terms of an arithmetic sequence:
\[
S_n = \frac{n}{2} \times (2a_1 + (n-1)d)
\]
Where:
- \(n\) is the number of terms.
- \(a_1\) is the first term.
- \(d\) is the common difference.

For the first five terms:
\[
S_5 = \frac{5}{2} \times (2(5) + (5-1)(3))
\]
\[
S_5 = \frac{5}{2} \times (10 + 12) = \frac{5}{2} \times 22 = 5 \times 11 = 55
\]

So, the sum of the numbers \(5, 8, 11, 14, 17\) is **55**.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you find the sum of the first \(n\) terms of any arithmetic sequence?
2. How can you determine the nth term of an arithmetic sequence?
3. What is the common difference in an arithmetic sequence, and how does it affect the sequence?
4. How do arithmetic sequences differ from geometric sequences?
5. Can you derive the formula for the sum of an arithmetic series?

**Tip:** Remember that the sum of an arithmetic series can be quickly calculated if you know the first and last terms, as an alternative formula is \(S_n = \frac{n}{2} \times (a_1 + a_n)\).

Learn how to calculate the sum of an arithmetic sequence 5, 8, 11, 14, 17. This problem involves finding the sum using the arithmetic sequence formula and understanding the concept of common difference. Suitable for students in Grades 7-9.

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