interval. ive completed the first several rows for you.

\begin{tabular}{|c|c|c|c|}
\hline
time & 5 minute interval \\ (n) & number of \\ people told & number of people \\ who know \\
\hline
12:00 & 0 & - & 1 \\
\hline
12:05 & 1 & 2 & 3 \\
\hline
12:10 & 2 & 2 & 5 \\
\hline
12:15 & 3 & & \\
\hline
12:20 & 4 & & \\
\hline
12:25 & 5 & & \\
\hline
12:30 & 6 & & \\
\hline
12:35 & 7 & & \\
\hline
12:40 & 8 & & \\
\hline
12:45 & 9 & & \\
\hline
12:50 & 10 & & \\
\hline
\end{tabular}

Question

interval. ive completed the first several rows for you.

\begin{tabular}{|c|c|c|c|}
\hline
time & 5 minute interval \\ (n) & number of \\ people told & number of people \\ who know \\
\hline
12:00 & 0 & - & 1 \\
\hline
12:05 & 1 & 2 & 3 \\
\hline
12:10 & 2 & 2 & 5 \\
\hline
12:15 & 3 & & \\
\hline
12:20 & 4 & & \\
\hline
12:25 & 5 & & \\
\hline
12:30 & 6 & & \\
\hline
12:35 & 7 & & \\
\hline
12:40 & 8 & & \\
\hline
12:45 & 9 & & \\
\hline
12:50 & 10 & & \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences", "Linear Growth" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Linear Growth" ] } ## Identify the pattern of growth $$ \begin{aligned} &n = 0: \text{Number of people told} = -, \text{Number of people who know} = 1 \ &n = 1: \text{Number of people told} = 2, \text{Number of people who know} = 3 \ &n = 2: \text{Number of people told} = 2, \text{Number of people who know} = 5 \end{aligned} $$ ## Formulate the recurrence relation $$ \begin{aligned} &\text{Number of people told at interval } n \ge 1: T(n) = 2 \ &\text{Number of people who know at interval } n: K(n) = K(n-1) + T(n) \ &K(n) = 1 + 2n \end{aligned} $$ ## Calculate the values for remaining intervals $$ \begin{aligned} &n = 3: T(3) = 2, K(3) = 7 \ &n = 4: T(4) = 2, K(4) = 9 \ &n = 5: T(5) = 2, K(5) = 11 \ &n = 6: T(6) = 2, K(6) = 13 \ &n = 7: T(7) = 2, K(7) = 15 \ &n = 8: T(8) = 2, K(8) = 17 \ &n = 9: T(9) = 2, K(9) = 19 \ &n = 10: T(10) = 2, K(10) = 21 \end{aligned} $$ The completed table is: | Time | 5 minute interval ($n$) | Number of people told | Number of people who know | | :---: | :---: | :---: | :---: | | 12:00 | 0 | — | 1 | | 12:05 | 1 | 2 | 3 | | 12:10 | 2 | 2 | 5 | | 12:15 | 3 | 2 | 7 | | 12:20 | 4 | 2 | 9 | | 12:25 | 5 | 2 | 11 | | 12:30 | 6 | 2 | 13 | | 12:35 | 7 | 2 | 15 | | 12:40 | 8 | 2 | 17 | | 12:45 | 9 | 2 | 19 | | 12:50 | 10 | 2 | 21 | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

Time	5 minute interval (\(n\))	Number of people told	Number of people who know
12:05	1	2	<blank>3</blank>
12:10	2	2	<blank>5</blank>
12:15	3	<blank>2</blank>	<blank>7</blank>
12:20	4	<blank>2</blank>	<blank>9</blank>
12:25	5	<blank>2</blank>	<blank>11</blank>
12:30	6	<blank>2</blank>	<blank>13</blank>
12:35	7	<blank>2</blank>	<blank>15</blank>
12:40	8	<blank>2</blank>	<blank>17</blank>
12:45	9	<blank>2</blank>	<blank>19</blank>
12:50	10	<blank>2</blank>	<blank>21</blank>

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QUESTION IMAGE

Question

Explanation:

Identify the pattern of growth

Formulate the recurrence relation

Calculate the values for remaining intervals

Answer: