Math Problem Statement

Assuming a linear relationship, find the missing value in the table below. | x | 1 | 2 | 3 | 4 | 5 | |----|----|----|----|----|----| | y | 9 | 12 | 15 | 18 | ? |

Solution

Let's analyze the pattern in the table:

x12345
y9121518?

Observing the y-values:

  • 9 → 12 (increase by 3)
  • 12 → 15 (increase by 3)
  • 15 → 18 (increase by 3)

Since this follows a linear pattern, the next value should be: 18+3=2118 + 3 = 21

Thus, the missing value in the table is 21.

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Related Questions:

  1. How can you determine if a sequence follows a linear pattern?
  2. What is the general formula for a linear sequence?
  3. How can you find a missing value in an arithmetic sequence?
  4. How do you calculate the common difference in a linear pattern?
  5. Can you derive a formula to find any term in this sequence?

Tip:

For a linear sequence, the general formula is: y=mx+by = mx + b where mm is the common difference, and bb is the y-intercept.

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Math Problem Analysis

Mathematical Concepts

Linear Relationships
Arithmetic Sequences

Formulas

y = mx + b
Arithmetic Sequence Formula: y = y_0 + (n-1) * d

Theorems

Linear Pattern
Common Difference

Suitable Grade Level

Grades 6-8