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Looking at the image, it seems you are working with an arithmetic progression (AP) and solving for the sum of its terms. From your question, you're asking why a specific calculation yields 84.

Let's break down the problem as it appears in your work:

1. **Given values:**
   - \( a = 9 \) (first term)
   - \( l = 71 \) (last term)
   - \( d = 7 \) (common difference)
   
2. **To find:** \( n \) (the number of terms)
   
   The formula for the \( n \)-th term of an arithmetic progression is:
   \[
   l = a + (n-1) \cdot d
   \]
   Substituting the known values:
   \[
   71 = 9 + (n-1) \cdot 7
   \]
   Solving for \( n \):
   \[
   71 - 9 = (n-1) \cdot 7
   \]
   \[
   62 = (n-1) \cdot 7
   \]
   \[
   n-1 = \frac{62}{7} = 8.857 \quad \text{(not an integer)}
   \]
   
   It seems there might be a rounding or transcription error in this particular step.

Could you clarify if you need help with this step, or if you would like to explore another part of the problem?

Why did the result become 84 in the given arithmetic progression problem?

Explore how to solve arithmetic progression problems, including finding the number of terms and the sum of terms. This problem involves key concepts in sequences and series, suitable for students in Grades 9-10.

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