Enter a recursive rule for the geometric sequence. 6, −18, 54, −162, ...
1 answer:
Answer:
The recursive formula needed is:
Detailed explanation:
We are given a geometric sequence:
6, -18, 54, -162, ...
By examining the terms, we see this sequence is a geometric progression (G.P.) with a common ratio, r, of -3.
Let denote the nth term.
This implies:
Since the common ratio equals -3,
therefore,
Thus, the recursive formula for this geometric sequence is:
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Response:
PQ's slope is 0
MN's slope equals infinity
The lines PQ and MN are perpendicular to one another
Detailed explanation:
For two points in the coordinate plane, denoted as (x1, y1) and (x2, y2), the slope is determined as follows:
If a line has a slope of zero, it runs parallel to the X-axis and stands perpendicular to the Y-axis
If a line's slope is infinite, it is parallel to the Y-axis and perpendicular to the X-axis
Moreover, it is established that X and Y are perpendicular to each other.
As PQ's slope is zero, it runs parallel to the X-axis and perpendicular to the Y-axis
With MN having an infinite slope, it runs parallel to the Y-axis and perpendicular to the X-axis.
Therefore, lines PQ and MN are indeed perpendicular.