Question

which statements are true for calculating the common ratio, r, based on the table of values? there is more than one correct answer choice. select all that apply. when the coordinates (2,2744) and (3,38416) are considered, $r=\frac{38416}{2744}=14$. when the coordinates (2,2744) and (4,537824) are considered, $r = \frac{537824}{2744}=196$. when the coordinates (5,7529536) and (6,105413504) are considered, $r=\frac{105413504}{7529536}=$ when the coordinates (1,196) and (3,38416) are considered, $r=\frac{38416}{196}=196$. when the coordinates (3,38416) and (5,7529536) are considered, $r=\frac{7529536}{38416}=196$. when the coordinates (1,196) and (2,2744) are considered, $r=\frac{2744}{196}=14$.

Explanation:

Step1: Recall common - ratio formula

For a geometric sequence, if we have two terms \((n_1,a_{n_1})\) and \((n_2,a_{n_2})\) with \(n_2>n_1\), the common ratio \(r = a_{n_2}/a_{n_1}\) when the sequence is geometric.

Step2: Check each option

Option 1:

Given \((2,2744)\) and \((3,38416)\), \(r=\frac{38416}{2744} = 14\).

Option 2:

Given \((2,2744)\) and \((4,537824)\), \(r=\frac{537824}{2744}=196\).

Option 3:

Given \((5,7529536)\) and \((6,105413504)\), \(r = \frac{105413504}{7529536}=14\).

Option 4:

Given \((1,196)\) and \((3,38416)\), \(r=\frac{38416}{196}=196\).

Option 5:

Given \((3,38416)\) and \((5,7529536)\), \(r=\frac{7529536}{38416}=196\).

Option 6:

Given \((1,196)\) and \((2,2744)\), \(r=\frac{2744}{196}=14\).

Answer:

When the coordinates \((2,2744)\) and \((3,38416)\) are considered, \(r = \frac{38416}{2744}=14\);
When the coordinates \((2,2744)\) and \((4,537824)\) are considered, \(r=\frac{537824}{2744}=196\);
When the coordinates \((1,196)\) and \((3,38416)\) are considered, \(r=\frac{38416}{196}=196\);
When the coordinates \((3,38416)\) and \((5,7529536)\) are considered, \(r=\frac{7529536}{38416}=196\);
When the coordinates \((1,196)\) and \((2,2744)\) are considered, \(r=\frac{2744}{196}=14\).