Question

if the first term of a geometric sequence is 7 and the third term is 112, what is the second term?

select one:
a. 28
b. 784
c. 448
d. 16

Explanation:

Step1: Recall geometric sequence formula

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

Step2: Set up equation for 3rd term

We know $a_1=7$, $a_3=112$. Substitute into formula:
$112 = 7 \times r^{3-1}$

Step3: Solve for common ratio $r$

First, divide both sides by 7:
$\frac{112}{7} = r^2$
$16 = r^2$
Take square root: $r = \pm 4$

Step4: Calculate 2nd term

Use $a_2 = a_1 r$:
If $r=4$, $a_2 = 7 \times 4 = 28$
If $r=-4$, $a_2 = 7 \times (-4) = -28$ (not an option)

Answer:

A. 28