In a geometric series, the sum of the first \( n \) terms can be calculated using the formula:
\[ S_n = a \frac{1 - r^n}{1 - r} \]
where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( a \) is the first term,
- \( r \) is the common ratio, and
- \( n \) is the number of terms.
Here, we have:
- \( a = 1 \)
- \( r = 1.5 \)
- \( n = 5 \)
Now, we can substitute these values into the formula:
\[ S_5 = 1 \frac{1 - (1.5)^5}{1 - 1.5} \]
First, calculate \( (1.5)^5 \):
\[ (1.5)^5 = 7.59375 \]
Now substitute this back into the sum:
\[ S_5 = 1 \frac{1 - 7.59375}{1 - 1.5} \] \[ = \frac{1 - 7.59375}{-0.5} \] \[ = \frac{-6.59375}{-0.5} = 13.1875 \]
Finally, rounding this to the nearest tenth:
\[ S_5 \approx 13.2 \]
Thus, the sum of the first 5 terms of the geometric series is \( \boxed{13.2} \).