find the sum of the first 92 terms of an arithmetic sequence whose first term is 12 and whose common difference is 13

To find the sum of the first 92 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:
- \( a = 12 \)
- \( d = 13 \)
- \( n = 92 \)

Substitute the values into the formula:

\[
S_{92} = \frac{92}{2} \times \left(2 \times 12 + (92-1) \times 13\right)
\]

\[
S_{92} = 46 \times \left(24 + 91 \times 13\right)
\]

\[
S_{92} = 46 \times \left(24 + 1183\right)
\]

\[
S_{92} = 46 \times 1207 = 55522
\]

So, the sum of the first 92 terms of the arithmetic sequence is **55,522**.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:
1. What is the 92nd term of this arithmetic sequence?
2. How would you find the sum of the first 50 terms of this sequence?
3. How does the sum change if the common difference is 10 instead of 13?
4. What is the formula to find the \(n\)th term of an arithmetic sequence?
5. Can you calculate the sum of the first 100 terms if the first term is 15 and the common difference is 8?

**Tip:** When dealing with large sequences, always carefully track the multiplication

Learn how to find the sum of the first 92 terms of an arithmetic sequence with a first term of 12 and a common difference of 13. This problem covers arithmetic sequences and series summation. Suitable for students in Grades 9-12.

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