QuestionJuly 23, 2025

The sum of the first four terms of a geometric series with a first term of 2 and a common ratio of 4 is 136. True False

The sum of the first four terms of a geometric series with a first term of 2 and a common ratio of 4 is 136. True False
The sum of the first four terms of a geometric series
with a first term of 2 and a common ratio of 4 is 136.
True
False

Solution
4.0(235 votes)

Answer

False Explanation 1. Identify the formula for the sum of a geometric series The sum of the first n terms of a geometric series is given by S_n = a \frac{r^n - 1}{r - 1}, where a is the first term and r is the common ratio. 2. Calculate the sum of the first four terms Substitute a = 2, r = 4, and n = 4 into the formula: S_4 = 2 \frac{4^4 - 1}{4 - 1} = 2 \frac{256 - 1}{3} = 2 \times 85 = 170.

Explanation

1. Identify the formula for the sum of a geometric series<br /> The sum of the first $n$ terms of a geometric series is given by $S_n = a \frac{r^n - 1}{r - 1}$, where $a$ is the first term and $r$ is the common ratio.<br />2. Calculate the sum of the first four terms<br /> Substitute $a = 2$, $r = 4$, and $n = 4$ into the formula: $S_4 = 2 \frac{4^4 - 1}{4 - 1} = 2 \frac{256 - 1}{3} = 2 \times 85 = 170$.
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