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The figures below represent the sequence [tex]\(\{7, 11, 15, 19, \ldots\}\)[/tex] and is generated by the function [tex]\(f(n) = 4n + 3\)[/tex] where [tex]\(n\)[/tex] is the figure number and [tex]\(f(n)\)[/tex] is the sum of the blocks in the figure. Complete the table below to determine how many blocks are in the [tex]\(5^{\text{th}}\)[/tex] figure.

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$n$ & 1 & 2 & 3 & 4 & 5 \\
\hline
$f(n)$ & 7 & 11 & 15 & 19 & 23 \\
\hline
$(n, f(n))$ & (1, 7) & (2, 11) & (3, 15) & (4, 19) & (5, 23) \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
To determine how many blocks are in the 5th figure using the function [tex]\( f(n) = 4n + 3 \)[/tex], let's proceed step by step.

1. Identify the sequence function: We are given the function [tex]\( f(n) = 4n + 3 \)[/tex], where [tex]\( n \)[/tex] is the figure number and [tex]\( f(n) \)[/tex] gives the number of blocks in the figure.

2. Calculate the number of blocks for each figure from [tex]\( n = 1 \)[/tex] to [tex]\( n = 5 \)[/tex]:
- For [tex]\( n = 1 \)[/tex]:
[tex]\[ f(1) = 4 \cdot 1 + 3 = 4 + 3 = 7 \][/tex]

- For [tex]\( n = 2 \)[/tex]:
[tex]\[ f(2) = 4 \cdot 2 + 3 = 8 + 3 = 11 \][/tex]

- For [tex]\( n = 3 \)[/tex]:
[tex]\[ f(3) = 4 \cdot 3 + 3 = 12 + 3 = 15 \][/tex]

- For [tex]\( n = 4 \)[/tex]:
[tex]\[ f(4) = 4 \cdot 4 + 3 = 16 + 3 = 19 \][/tex]

- For [tex]\( n = 5 \)[/tex]:
[tex]\[ f(5) = 4 \cdot 5 + 3 = 20 + 3 = 23 \][/tex]

3. Complete the table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|} \hline n & 1 & 2 & 3 & 4 & 5 \\ \hline f(n) & 7 & 11 & 15 & 19 & 23 \\ \hline (n, f(n)) & (1, 7) & (2, 11) & (3, 15) & (4, 19) & (5, 23) \\ \hline \end{tabular} \][/tex]

4. Answer: The number of blocks in the [tex]\( 5^{\text{th}} \)[/tex] figure is [tex]\( 23 \)[/tex].

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