Q 5. Which linear function defines the arithmetic sequence $$ a_{n}=\{-5,-3,-1,1,3, \ldots\} $$ ? $$ a_{n}=5+2(n-1) $$ $$ a_{n}=5-2(n-1) $$ $$ a_{n}=-5+2(n-1) $$ $$ a_{n}=-5-2(n-1) $$

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To determine the linear function that defines the arithmetic sequence $$ a_{n} = \{-5, -3, -1, 1, 3, \ldots\} $$, we can use the formula for the $$ n $$-th term of an arithmetic sequence:

$$
a_{n} = a_1 + (n - 1)d
$$

where:
- $$ a_1 $$ is the first term of the sequence.
- $$ d $$ is the common difference between consecutive terms.

**Step 1: Identify $$ a_1 $$ and $$ d $$**

- The first term $$ a_1 = -5 $$.
- The common difference $$ d $$ can be found by subtracting the first term from the second term:
  $$
  d = a_2 - a_1 = (-3) - (-5) = 2
  $$

**Step 2: Substitute $$ a_1 $$ and $$ d $$ into the formula**

$$
a_{n} = -5 + 2(n - 1)
$$

This matches one of the provided options.

**Final Answer:**
$$
a_{n} = -5 + 2(n-1)
$$

**Answer:** $$ a_{n}=-5+2(n-1) $$
$$ a_{n} = -5 + 2(n-1) $$

Q 5. Which linear function defines the arithmetic sequence ?

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