The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ Find the third term
A) $a _ { 1 } = \frac { 1 } { 3 }$

B) $a _ { 1 } = \frac { 7 } { 3 }$

C) $a _ { 1 } = \frac { 3 } { 7 }$

D) $a _ { 1 } = \frac { 5 } { 3 }$

E) $a _ { 1 } = \frac { 2 } { 7 }$

Question

The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ Find the third term
A) $a _ { 1 } = \frac { 1 } { 3 }$

B) $a _ { 1 } = \frac { 7 } { 3 }$

C) $a _ { 1 } = \frac { 3 } { 7 }$

D) $a _ { 1 } = \frac { 5 } { 3 }$

E) $a _ { 1 } = \frac { 2 } { 7 }$

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$, where $a_n$ is the nth term, $a_1$ is the first term, and $r$ is the common ratio. Given the fourth term $a_4 = \frac{1}{7}$ and the common ratio $r = \frac{3}{7}$, we can find the first term $a_1$ by rearranging the formula: $a_1 = \frac{a_4}{r^{(4-1)}} = \frac{\frac{1}{7}}{(\frac{3}{7})^3} = \frac{1}{7} \cdot \frac{7^3}{3^3} = \frac{1}{7} \cdot \frac{343}{27} = \frac{49}{27}$. However, none of the options match this calculation, indicating a mistake in my explanation. Correctly, to find the third term, we use the formula $a_n = a_1 \cdot r^{(n-1)}$, but since the question and options seem to be mismatched regarding finding the first term or the third term, let's correctly address finding the third term given the fourth term is $\frac{1}{7}$ and the common ratio is $\frac{3}{7}$. The third term $a_3$ can be found by dividing the fourth term by the common ratio: $a_3 = \frac{a_4}{r} = \frac{\frac{1}{7}}{\frac{3}{7}} = \frac{1}{3}$, which matches option A if we were correctly asked to find the first term based on a misunderstanding of the question's intent. The correct approach to find the third term directly from the given information would involve using the formula $a_3 = a_4 / r = \frac{1}{7} / \frac{3}{7} = \frac{1}{3}$, but this calculation was intended to clarify the confusion in the explanation process.

The Common Ratio of a Geometric Sequence Is 37\frac { 3 } { 7 }73​

The Common Ratio of a Geometric Sequence Is $\frac { 3 } { 7 }$