Write an expression for this arithmetic sequence: $$ 16.5,19,21.5,24,26.5 \ldots $$ $$ \begin{array}{l}a_{n}=14+2.5(n-1) \ a_{n}=16.5+2.5(n-1) \ a_{n}=2.5 n+16.5 \ a_{n}=19+2.5 n\end{array} $$

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To find an expression for the given arithmetic sequence:

$$ 16.5, \, 19, \, 21.5, \, 24, \, 26.5, \ldots $$

**Step 1: Identify the First Term and Common Difference**

- **First term ($$a_1$$)**: $$16.5$$
- **Common difference ($$d$$)**: $$19 - 16.5 = 2.5$$

**Step 2: Use the General Formula for an Arithmetic Sequence**

The general formula for the $$n$$th term of an arithmetic sequence is:

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

Substituting the known values:

$$
a_n = 16.5 + 2.5(n - 1)
$$

**Step 3: Verify Against the Given Options**

Let's check the provided options to see which one matches our derived formula:

1. $$a_n = 14 + 2.5(n - 1)$$  
   - For $$n = 1$$: $$14 + 2.5(0) = 14$$ (Incorrect, since $$a_1 = 16.5$$)
   
2. $$a_n = 16.5 + 2.5(n - 1)$$  
   - For $$n = 1$$: $$16.5 + 2.5(0) = 16.5$$ (Correct)
   - For $$n = 2$$: $$16.5 + 2.5(1) = 19$$ (Correct)
   
3. $$a_n = 2.5n + 16.5$$  
   - For $$n = 1$$: $$2.5(1) + 16.5 = 19$$ (Incorrect, since $$a_1 = 16.5$$)
   
4. $$a_n = 19 + 2.5n$$  
   - For $$n = 1$$: $$19 + 2.5(1) = 21.5$$ (Incorrect, since $$a_1 = 16.5$$)

**Conclusion**

The correct expression for the arithmetic sequence is:

$$
a_n = 16.5 + 2.5(n - 1)
$$

**Answer:** 
$$ a_{n}=16.5+2.5(n-1) $$
The correct expression for the arithmetic sequence is: $$ a_{n} = 16.5 + 2.5(n - 1) $$

Write an expression for this arithmetic sequence:

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