This problem asks us to find the number of terms in an arithmetic sequence where the sum of all terms is given. Let's solve it step by step.

Given:

• First term ($a$) = 124
• Last term ($l$) = 111
• Sum of all terms ($S_n$) = 4700
• Formula for the sum of an arithmetic sequence:
  $S_n = \frac{n}{2} \cdot (a + l)$

Step 1: Substitute known values into the formula:

$4700 = \frac{n}{2} \cdot (124 + 111)$

Step 2: Simplify the equation:

$4700 = \frac{n}{2} \cdot 235$

Multiply both sides by 2: $9400 = n \cdot 235$

Step 3: Solve for $n$:

$n = \frac{9400}{235} = 40$

Final Answer:

The number of terms in the sequence is 40.

Would you like me to go into more detail on any part of this solution?

Related Questions:

1. What is the common difference of the sequence?
2. How do you find the $n$-th term of an arithmetic sequence?
3. What happens if the sum is a different value, e.g., $5000$?
4. How can you verify the number of terms once calculated?
5. How would the solution change if only the sum and first term were given?

Tip:

In arithmetic sequences, double-check calculations involving the sum formula by ensuring all terms align with the given series endpoints.