This is an arithmetic sequence, and to find the sum, let's go through the following steps:

1. **Identify the first term (\( a_1 \))**: The first term is \(-111\).
2. **Identify the common difference (\( d \))**:  
   Since the sequence consists of consecutive numbers increasing by 9 each time,  
   \( -111 + (-102) = -111 + 9 = -102 \).  
   So, the common difference \( d = 9 \).
3. **Find the last term (\( a_n \))**: The last term given is \( 168 \).
4. **Find the number of terms (\( n \))**:  
   The formula for the \( n \)-th term of an arithmetic sequence is:  
   \[
   a_n = a_1 + (n - 1) \cdot d
   \]  
   Plugging in the values:  
   \[
   168 = -111 + (n - 1) \cdot 9
   \]  
   Solve for \( n \):
   \[
   168 + 111 = (n - 1) \cdot 9
   \]
   \[
   279 = (n - 1) \cdot 9
   \]
   \[
   \frac{279}{9} = n - 1
   \]
   \[
   31 = n - 1
   \]
   \[
   n = 32
   \]

5. **Find the sum of the sequence (\( S_n \))**:  
   The sum of the first \( n \) terms of an arithmetic sequence is given by:
   \[
   S_n = \frac{n}{2} \times (a_1 + a_n)
   \]
   Plugging in the values:
   \[
   S_{32} = \frac{32}{2} \times (-111 + 168)
   \]
   \[
   S_{32} = 16 \times 57
   \]
   \[
   S_{32} = 912
   \]

So, the sum of the sequence is **912**.

Do you want details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you find the sum of an arithmetic sequence if the common difference is negative?
2. What happens to the sum if you change the common difference in an arithmetic sequence?
3. How would you derive the formula for the sum of an arithmetic sequence?
4. Can you find the sum of this sequence by manually adding each term?
5. What is the sum of an arithmetic sequence with only one term?

**Tip:** Always verify the common difference in an arithmetic sequence before proceeding with calculations.

Discover how to find the sum of the arithmetic sequence starting from -111 with a common difference of 9, and a last term of 168. This problem covers key mathematical concepts, including arithmetic sequences, the nth term formula, and summation of series. Suitable for students in Grades 9-10.

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