Math Problem Statement

Complete the table by identifying patterns and filling in the missing values.

Solution

The task involves completing the table shown in the uploaded image. To solve this, let's analyze the relationship between the numbers in the table. I'll extract the relevant data and determine the pattern or mathematical relationship.

Observations:

  1. The first column includes numbers like 161, 483, 644, 805, and there’s a blank square to fill.
  2. The second column includes numbers like 73, 146, 219, 292, and there’s a blank square to fill.

Let’s identify the pattern:

First Column vs. Second Column Relationship:

  • Comparing the first pair: 161161 and 7373: Difference: 16173=88\text{Difference: } 161 - 73 = 88
  • Comparing the second pair: 483483 and 219219: 483219=264(This is three times 88: 88×3)483 - 219 = 264 \quad (\text{This is three times 88: } 88 \times 3)
  • Comparing the third pair: 644644 and 292292: 644292=352(This is four times 88: 88×4)644 - 292 = 352 \quad (\text{This is four times 88: } 88 \times 4)

From these calculations, the differences appear to follow a proportional sequence based on multiples of 88.

Missing Values:

For the blank cells, let’s continue the sequence:

  • In the first column, the sequence increments by approximately +161,+161,+161+161, +161, +161. If this trend holds:

    • After 805805, the next value is: 805+161=966805 + 161 = 966
  • In the second column, the sequence increments by +73,+73,+73+73, +73, +73. If this trend holds:

    • After 292292, the next value is: 292+73=365292 + 73 = 365

Completed Table:

\hline 161 & 73 \\ 483 & 146 \\ 644 & 219 \\ 805 & 292 \\ 966 & 365 \\ \hline \end{array}$$ Let me know if you'd like further clarification or a different approach! --- ### Follow-up Questions: 1. What additional patterns might exist in the table if other columns were added? 2. Can this sequence be modeled using a mathematical formula? 3. How would you approach a scenario where the increments were not consistent? 4. What practical applications can you derive from analyzing such numeric patterns? 5. Are there any alternative methods to find the missing numbers apart from observing differences? ### Tip: When working with sequences, always check for common differences, ratios, or proportional relationships—they often reveal the underlying rule!

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Patterns and Relationships

Formulas

Arithmetic difference (Common Difference)
Increment Rule for Sequences

Theorems

Arithmetic Sequence Formula

Suitable Grade Level

Grades 6-8