Question

assuming a linear relationship, find the missing value in the table below. \\(\

$$\begin{array}{|c|c|c|c|c|c|} \\hline x & 1 & 2 & 3 & 4 & 5 \\\\ \\hline y & 3 & 10 & 17 & 24 & \\\\ \\hline \\end{array}$$

\\)

Explanation:

Step1: Find the common difference

To determine the common difference between consecutive \( y \)-values, we subtract the previous \( y \)-value from the next one. For example, \( 10 - 3 = 7 \), \( 17 - 10 = 7 \), and \( 24 - 17 = 7 \). So the common difference \( d = 7 \).

Step2: Calculate the missing \( y \)-value

To find the \( y \)-value when \( x = 5 \), we add the common difference to the previous \( y \)-value (when \( x = 4 \), \( y = 24 \)). So we calculate \( 24 + 7 = 31 \).

Answer:

The missing value is \( 31 \).