To find the 57th term of the given arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

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

Where:

• $a_n$ is the nth term.
• $a_1$ is the first term of the sequence.
• $d$ is the common difference between consecutive terms.
• $n$ is the position of the term in the sequence.

Step 1: Identify the first term and common difference

• The first term $a_1 = -13$.

• The common difference $d$ is the difference between any two consecutive terms:

  $d = -29 - (-13) = -29 + 13 = -16$

Step 2: Apply the formula for the 57th term

Now, using $a_1 = -13$, $d = -16$, and $n = 57$, substitute these values into the formula:

$a_{57} = -13 + (57-1) \cdot (-16)$

$a_{57} = -13 + 56 \cdot (-16)$

$a_{57} = -13 + (-896)$

$a_{57} = -909$

Final Answer:

The 57th term of the sequence is $\boxed{-909}$.

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Would you like further details on how the arithmetic sequence works, or do you have any other questions about sequences?

Here are some related questions you may find interesting:

1. What is the 100th term of the same arithmetic sequence?
2. How do we find the sum of the first 57 terms of this sequence?
3. What is the general formula for the sum of an arithmetic sequence?
4. How do you determine if a given sequence is arithmetic?
5. How does the common difference affect the shape of an arithmetic sequence?

Tip: When dealing with arithmetic sequences, always ensure you clearly identify the first term and common difference before using the formula for the nth term.