Question

Instructions: Select the appropriate explicit rule for the given sequence.

Answer 1

Given the sequence:

-18, -8, 2, 12, ...

Let's select the appropriate explicit rule.

Let's first confirm if the sequence is an arithmetic sequence by finding the common difference.

The common difference, is the difference between terms.

We have:

• d = a2 - a1 = 8 - (-18) = -8 + 18 = 10

,

• d = a3 - a2 = 2 - (-8) = 2 + 8 = 10

,

• d = a4 - a3 = 12 - 2 = 10

,

•

We can see the difference between consecutive terms is constant.

Since the difference is constant, the sequence is an arithmetic sequence wth acommon difference, d = 10.

Now, aply the explicit formula for arithmetic sequence:

$a_n=a_1+(n-1)d$

Where:

a1 is the first term = -18

d is the common difference = 10

Now, plug in the values in the formula and simplify:

$\begin{gathered} a_n=-18+(n-1)10 \\ \\ a_n=-18+10n-10 \\ \\ a_n=-18-10+10n \\ \\ a_n=-28+10n \end{gathered}$

Therefore, the appropriate explicit rue for hthe given sequence is:

$a_n=-28+10n$

ANSWER:

$a_{n}=-28+10n$