some of terms in a geometric sequence a for each given geometric sequence find the sum of the first number two 3/ -6/ 12/ -24​

Answer:To find the sum of the first 5 terms of the geometric sequence 3, -6, 12, -24, ..., we'll use the formula for the sum of a finite geometric series:$$S_n = \frac{a(1 - r^n)}{1 - r}$$where:- $S_n$ is the sum of the first n terms- $a$ is the first term (3 in this case)- $r$ is the common ratio (-2 in this case, since each term is -2 times the previous term)- $n$ is the number of terms (5 in this case)## Step 1: Identify the given values$a = 3$, $r = -2$, and $n = 5$.## Step 2: Plug the values into the formula$$S_5 = \frac{3(1 - (-2)^5)}{1 - (-2)}$$## Step 3: Simplify the expression$$S_5 = \frac{3(1 - (-32))}{1 + 2}$$$$S_5 = \frac{3(1 + 32)}{3}$$$$S_5 = \frac{3(33)}{3}$$$$S_5 = 33$$The final answer is: $\boxed{33}$

Answered by aldrinpenas85 | 2025-08-04