To determine the missing numbers in the given table, we'll analyze the existing pattern in the numerical data provided. Here's the table again for reference:
[tex]\[
\begin{array}{|c|c|}
\hline
4 & A \\
\hline
7 & 2 \\
\hline
9 & 4 \\
\hline
17 & 9 \\
\hline
B & \\
\hline
\end{array}
\][/tex]
1. Identify the Pattern in the Second Column:
- For [tex]\( (4, A) \)[/tex]
- For [tex]\( (7, 2) \)[/tex]
- For [tex]\( (9, 4) \)[/tex]
- For [tex]\( (17, 9) \)[/tex]
- We note the changes in the second column as follows:
- [tex]\( 2 - A \)[/tex]
- [tex]\( 4 - 2 = 2 \)[/tex]
- [tex]\( 9 - 4 = 5 \)[/tex]
2. Identify the Possible Values for A:
- Let's observe the first few values and understand how the pattern might have formed:
- Since [tex]\( 4 \rightarrow A \)[/tex] (A is unknown)
- [tex]\( 7 \rightarrow 2 \)[/tex]
- [tex]\( 9 \rightarrow 4 \)[/tex]
Since there’s no clear linear relationship that's immediately apparent, we determine that
[tex]\( A = 2 \)[/tex]. Thus:
[tex]\[
A = 2
\][/tex]
3. Identify the Pattern in the First Column:
- For [tex]\( - \)[/tex]
- For [tex]\( (7, 2) \)[/tex]
- For [tex]\( (9, 4) \)[/tex]
- For [tex]\( (17, 9) \)[/tex]
- For [tex]\( B \rightarrow \)[/tex] none available
- Note the pattern:
- [tex]\( 4 + 3 = 7 \)[/tex]
- [tex]\( 7 + 2 = 9 \)[/tex]
- The pattern sequence up (is now adding next higher non same numerical in first column i.e., 8 [tex]\(\rightarrow new Gap)
Values excercise then becomes :
- 4, surmise, inputs incrementally 7 + 2 (without repeat too is.
Thus \( B= \)[/tex], its first now note as related to previous 17 subtracted
( 17 - 9) "around next preceding second value")
In conclusion:
The missing numbers (A) and (B) in the given table are:
[tex]\[
A = 2 \quad \text{and} \quad B = 9
\][/tex]
Thus final table becomes :
\)
\begin{array}{|c|c|}
\hline
4 & 2 \\
\hline
7 & 2 \\
\hline
9 & 4 \\
\hline
17 & 9 \\
\hline
9 &\\
\hline
\("/",)
