https://file.aiquickdraw.com/mathbot/file/1725512990206ugz5gam5.jpg

The problem presented in the image asks to "Write a formula for the sequence below, then find a₆."

The sequence given is:

\[ 5, 3, 1, -1, \dots \]

### Step 1: Identify the pattern
The difference between consecutive terms:
- \( 5 - 3 = 2 \)
- \( 3 - 1 = 2 \)
- \( 1 - (-1) = 2 \)

So, this is an **arithmetic sequence** with a common difference \( d = -2 \).

### Step 2: General formula for an arithmetic sequence
The general formula for an arithmetic sequence is:

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

Where:
- \( a_1 = 5 \) (the first term)
- \( d = -2 \) (the common difference)

### Step 3: Find the formula
Substitute \( a_1 \) and \( d \) into the formula:

\[
a_n = 5 + (n - 1) \cdot (-2)
\]

Simplify:

\[
a_n = 5 - 2(n - 1)
\]
\[
a_n = 5 - 2n + 2
\]
\[
a_n = 7 - 2n
\]

### Step 4: Find \( a_6 \)
To find \( a_6 \), substitute \( n = 6 \) into the formula:

\[
a_6 = 7 - 2(6) = 7 - 12 = -5
\]

Thus, \( a_6 = -5 \).

Would you like further explanation or have any questions?

### Related Questions:
1. What is the formula for the nth term of a geometric sequence?
2. How can you find the sum of the first n terms of an arithmetic sequence?
3. How do you derive the common difference of an arithmetic sequence from two terms?
4. What happens if the common difference of a sequence is 0?
5. Can arithmetic sequences have fractional or decimal common differences?

**Tip:** Always check the first few terms of a sequence to identify if it's arithmetic or geometric before finding a general formula!

Write a formula for the sequence: 5, 3, 1, -1,..., then find a₆.

Learn how to find the general formula for the arithmetic sequence 5, 3, 1, -1,... and calculate the 6th term (a₆). This detailed step-by-step solution involves the concept of arithmetic progression and algebraic formulas, suitable for students in Grades 7-9.

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