Find the sum of this 35 terms arithmetic sequence 4,7,10,13,…..
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2 puntos
1825
1910
1925
1935

To find the sum of the first 35 terms of the arithmetic sequence, we can use the formula for the sum of an arithmetic sequence:

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

where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( n \) is the number of terms,
- \( a_1 \) is the first term, and
- \( a_n \) is the last term.

### Step 1: Identify the given values
- First term \( a_1 = 4 \)
- Number of terms \( n = 35 \)
- Common difference \( d = 7 - 4 = 3 \)

### Step 2: Find the 35th term (\( a_{35} \))
The \( n \)-th term of an arithmetic sequence is given by:

\[
a_n = a_1 + (n - 1) \times d
\]

Substitute the values:

\[
a_{35} = 4 + (35 - 1) \times 3 = 4 + 34 \times 3 = 4 + 102 = 106
\]

### Step 3: Calculate the sum of the first 35 terms
Now, use the sum formula:

\[
S_{35} = \frac{35}{2} \times (4 + 106) = \frac{35}{2} \times 110 = 35 \times 55 = 1925
\]

So, the sum of the first 35 terms is **1925**.

Would you like more details or have any questions?

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Here are five related questions:
1. What would be the sum of the first 50 terms of this sequence?
2. How do you determine the common difference in an arithmetic sequence?
3. What is the sum of the first 20 terms of an arithmetic sequence with a common difference of 5 and a first term of 2?
4. How can you find the number of terms needed to reach a certain sum in an arithmetic sequence?
5. How does the sum formula change if the sequence is geometric instead of arithmetic?

**Tip:** Always double-check your calculations, especially when dealing with large numbers, to avoid simple mistakes.

Learn how to find the sum of the first 35 terms in the arithmetic sequence 4, 7, 10, 13, ... with a step-by-step solution. This problem involves calculating the sum using the formula for an arithmetic sequence. Suitable for students in Grades 9-12.

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