Question

the table shows an arithmetic sequence.

how could you find the missing value in the table?
check all that apply.

evaluate the explicit rule for \\(n = 4\\).
add 36 to the third term of the sequence.
subtract 16 from the fifth term of the sequence.

Explanation:

Find the common difference

Using the Arithmetic Sequences knowledge point

$$ d = a_2 - a_1 = 52 - 36 = 16 $$

Determine the explicit rule

Using the Arithmetic Sequence Explicit Formula knowledge point

$$
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$$

Analyze the first option

Using the Arithmetic Sequence Explicit Formula knowledge point

$$ a_4 = 16(4) + 20 = 84 $$

This method is valid.

Analyze the second option

Using the Arithmetic Sequences knowledge point

$$ a_4 = a_3 + d = 68 + 16 = 84 e 68 + 36 $$

This method is invalid.

Analyze the third option

Using the Arithmetic Sequences knowledge point

$$ a_4 = a_5 - d = 100 - 16 = 84 $$

This method is valid.

Answer:

• Evaluate the explicit rule for \(n = 4\). (Correct answer)
• Add 36 to the third term of the sequence.
• Subtract 16 from the fifth term of the sequence. (Correct answer)