The first sum of the 12 terms in the given series 1.5-4.5+13.5+40.5- is 161,631.
The given series is: 1.5-4.5+13.5+40.5-
To find the sum of the first 12 terms in this series, we can follow these steps:
1. Identify the pattern: To find the sum of the series, we need to identify the pattern followed by the terms. Looking at the given series, we can see that each term alternates between positive and negative signs and increases by a factor of 3. The first term is 1.5, and each subsequent term is obtained by multiplying the previous term by 3.
2. Write out the terms: Let's write out the first 12 terms of the series to understand it better:
1.5, -4.5, 13.5, 40.5, -121.5, 364.5, -1093.5, 3280.5, -9841.5, 29524.5, -88573.5, 265720.5
3. Find the sum: Now, let's add up the first 12 terms:
1.5 + (-4.5) + 13.5 + 40.5 + (-121.5) + 364.5 + (-1093.5) + 3280.5 + (-9841.5) + 29524.5 + (-88573.5) + 265720.5
The sum of these terms is 161,631.