Question

the table shows an arithmetic sequence.

\\(\

$$\begin{array}{|c|c|c|c|c|c|}\\hline n & 1 & 2 & 3 & 4 & 5 \\\\\\hline a_n & 36 & 52 & 68 & ? & 100 \\\\\\hline\\end{array}$$

\\)

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.

what is the explicit rule for the sequence?

• \\(a_n = -16 + (n - 1)36\\)
• \\(a_n = 16 + (n - 1)36\\)
• \\(a_n = 36 + (n - 1)(-16)\\)
• \\(a_n = 36 + (n - 1)16\\)

Explanation:

Identify the first term and common difference

Using the Arithmetic Sequences knowledge point

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Write the explicit formula

Using the Arithmetic Sequence Explicit Formula knowledge point

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$$

Answer:

• (A) \(a_n = -16 + (n - 1)36\)
• (B) \(a_n = 16 + (n - 1)36\)
• (C) \(a_n = 36 + (n - 1)(-16)\)
• (D) \(a_n = 36 + (n - 1)16\) (Correct answer)