To determine the sum of the sequence $9 + 6 + 4 + \ldots$, we first need to identify the type of sequence and its properties.

Step 1: Identify the sequence

This appears to be an arithmetic sequence, as each term decreases by a constant value. Let's verify:

• First term ($a$) = 9
• Second term = 6
• Difference ($d$) = $6 - 9 = -3$

Step 2: General formula for the $n$-th term

The formula for the $n$-th term of an arithmetic sequence is: $a_n = a + (n - 1)d$

For this sequence: $a_n = 9 + (n - 1)(-3)$ $a_n = 9 - 3n + 3 = 12 - 3n$

Step 3: Find the last term ($a_n$) if the sum is finite

The sum of the sequence will depend on the number of terms ($n$) or the point at which the sequence ends. If no stopping condition is provided, it could go to infinity, making the sum undefined.

• If you have more context (e.g., a last term, $a_n = 0$), provide it.

Would you like me to solve with specific stopping conditions? Let me know! Below are 5 related questions to expand your understanding.

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1. How do you calculate the sum of an arithmetic sequence with a fixed number of terms?
2. What happens when the sequence is infinite but does not converge?
3. How do you derive the formula for the sum of an arithmetic series?
4. Can you explain the difference between arithmetic and geometric sequences?
5. How does the common difference ($d$) affect the progression of the sequence?

Tip: Always verify the type of sequence before attempting to calculate its sum.