The given table represents a sequence where each term $a_n$ is related to its position $n$ in the sequence. To find the missing terms, we need to identify the pattern or rule of the sequence.

Looking at the given terms, it seems like each term $a_n$ is $3$ times the square of its position $n$. This is because $3*1^2=3$, $3*2^2=12$, $3*3^2=27$, $3*4^2=48$, and $3*5^2=75$.

So, to find the missing terms for $n=6, 7, 8$, we can use the rule $a_n = 3n^2$:

- For $n=6$, $a_n = 3*6^2 = 108$.
- For $n=7$, $a_n = 3*7^2 = 147$.
- For $n=8$, $a_n = 3*8^2 = 192$.

So, the completed table is:

$n$ 1 2 3 4 5 6 7 8
$a_n$ 3 12 27 48 75 108 147 192

Question

The given table represents a sequence where each term $a_n$ is related to its position $n$ in the sequence. To find the missing terms, we need to identify the pattern or rule of the sequence.

Looking at the given terms, it seems like each term $a_n$ is $3$ times the square of its position $n$. This is because $3*1^2=3$, $3*2^2=12$, $3*3^2=27$, $3*4^2=48$, and $3*5^2=75$.

So, to find the missing terms for $n=6, 7, 8$, we can use the rule $a_n = 3n^2$:

- For $n=6$, $a_n = 3*6^2 = 108$.
- For $n=7$, $a_n = 3*7^2 = 147$.
- For $n=8$, $a_n = 3*8^2 = 192$.

So, the completed table is:

$n$	1	2	3	4	5	6	7	8
$a_n$	3	12	27	48	75	108	147	192

Knowee AI · Accepted Answer

The given table represents a sequence where each term $a_n$ is related to its position $n$ in the sequence. To find the missing terms, we need to identify the pattern or rule of the sequence.

Looking at the given terms, it seems like each term $a_n$ is $3$ times the square of its position $n$. This is because $3*1^2=3$, $3*2^2=12$, $3*3^2=27$, $3*4^2=48$, and $3*5^2=75$.

So, to find the missing terms for $n=6, 7, 8$, we can use the rule $a_n = 3n^2$:

- For $n=6$, $a_n = 3*6^2 = 108$.
- For $n=7$, $a_n = 3*7^2 = 147$.
- For $n=8$, $a_n = 3*8^2 = 192$.

So, the completed table is:

$n$	1	2	3	4	5	6	7	8
$a_n$	3	12	27	48	75	108	147	192

b. Complete the table.$n$n 1 2 3 4 5 6 7 8$a_n$an 3 12 27 48 75

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b. Complete the table.$n$n​ 1 2 3 4 5 6 7 8$a_n$an​​ 3 12 27 48 75

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b. Complete the table.$n$n 1 2 3 4 5 6 7 8$a_n$an 3 12 27 48 75