To find the sum of an arithmetic series, we use the formula:

$S_n = \frac{n}{2} \cdot (a + l)$

Where:

• $S_n$ is the sum of the series.
• $n$ is the number of terms.
• $a$ is the first term.
• $l$ is the last term.

Given:

• $a = 1.5$ (first term)
• $l = 4.5$ (last term)
• $n$ (number of terms) can be determined from the sequence:
  • The terms increase by $d = 0.3$ (common difference).
  • To find $n$, use the formula for the $n$-th term of an arithmetic sequence: $a_n = a + (n-1) \cdot d$ Substituting $a_n = 4.5$, $a = 1.5$, and $d = 0.3$: $4.5 = 1.5 + (n-1) \cdot 0.3$ Simplifying: $4.5 - 1.5 = 0.3 \cdot (n-1) \implies 3 = 0.3 \cdot (n-1)$ $n-1 = 10 \implies n = 11$

Thus, there are 11 terms.

Calculate the Sum:

Substitute $n = 11$, $a = 1.5$, and $l = 4.5$ into the sum formula: $S_n = \frac{11}{2} \cdot (1.5 + 4.5)$ $S_n = \frac{11}{2} \cdot 6 = 11 \cdot 3 = 33$

Final Answer:

The sum of the arithmetic series is: $\boxed{33}$

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Would you like further details or have additional questions?
Here are 5 related questions to explore:

1. How do you derive the formula for the sum of an arithmetic series?
2. What happens if the common difference is negative?
3. How can you verify the sum by manually adding all terms?
4. How do you find the sum if the sequence is given in reverse?
5. Can you apply this formula to an infinite arithmetic sequence?

Tip: Always check the number of terms carefully when working with sequences.