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The problem in the image asks to find the 96th term of the arithmetic sequence: \( 4, -5, -14, \dots \).

### Step-by-step solution:

In an arithmetic sequence, the formula for the \(n\)-th term is given by:

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

where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

From the sequence \(4, -5, -14, \dots\):
- \(a_1 = 4\),
- The common difference \(d\) is the difference between consecutive terms: 
  \[
  d = -5 - 4 = -9
  \]

Now, to find the 96th term (\(a_{96}\)):

\[
a_{96} = a_1 + (96 - 1) \cdot d
\]
\[
a_{96} = 4 + 95 \cdot (-9)
\]
\[
a_{96} = 4 - 855
\]
\[
a_{96} = -851
\]

So, the 96th term of the sequence is \(-851\).

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Let me know if you'd like more details, or if you have any other questions. Here are five related questions to explore:

1. How do you find the common difference in any arithmetic sequence?
2. What is the formula for the sum of the first \(n\) terms in an arithmetic sequence?
3. How would you find the 150th term in the same sequence?
4. What is the 10th term of this sequence?
5. Can an arithmetic sequence have increasing terms? If so, what condition must hold?

**Tip:** Always ensure to identify both the first term and common difference clearly when solving for terms in an arithmetic sequence.

Find the 96th term of the arithmetic sequence: 4, -5, -14, ...

Learn how to find the 96th term of the arithmetic sequence 4, -5, -14, ... using the nth term formula. Step-by-step explanation included for students in Grades 7-10.

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