If a_1 is 36 and the common difference is -7 what’s the general formula

The problem gives the first term \( a_1 = 36 \) and the common difference \( d = -7 \) for an arithmetic sequence.

The general formula for the \( n \)-th term of an arithmetic sequence is:

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

Substituting the given values \( a_1 = 36 \) and \( d = -7 \), we get:

\[
a_n = 36 + (n - 1) \cdot (-7)
\]

Simplifying:

\[
a_n = 36 - 7(n - 1)
\]
\[
a_n = 36 - 7n + 7
\]
\[
a_n = 43 - 7n
\]

Thus, the general formula for the arithmetic sequence is:

\[
a_n = 43 - 7n
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the sum of the first \( n \) terms of this sequence?
2. What is the 10th term of the sequence?
3. How do you identify whether a number is part of this arithmetic sequence?
4. How does the sequence behave as \( n \) increases?
5. How would the formula change if the common difference were positive?

**Tip:** In arithmetic sequences, each term differs from the previous one by a constant value called the common difference.

If a_1 is 36 and the common difference is -7, what’s the general formula?

Find the general formula for an arithmetic sequence where the first term is 36 and the common difference is -7. This step-by-step guide explains the formula a_n = 43 - 7n, covering key concepts in arithmetic sequences and linear equations. Ideal for students in Grades 7-9.

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