Question

in a geometric sequence, the first term, $a_1$, is equal to 7, and the fourth term, $a_4$, is equal to 56. which number could represent the common ratio of the geometric sequence?
answer
$r = 0$
$r = 1$
$r = 2$
$r = 3$
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Explanation:

Step1: Recall geometric sequence formula

The nth term of a geometric sequence is given by $a_n = a_1 r^{n-1}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.

Step2: Plug in known values

We know $a_1=7$, $a_4=56$, and $n=4$. Substitute into the formula:
$56 = 7 \times r^{4-1}$

Step3: Simplify and isolate $r^3$

Divide both sides by 7:
$\frac{56}{7} = r^3$
$8 = r^3$

Step4: Solve for $r$

Take the cube root of both sides:
$r = \sqrt[3]{8}$
$r=2$

Answer:

$r = 2$