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Step-by-step explanation:
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Answer:
4.5, -27, 162,-972, 5832
Step-by-step explanation:
The given recursive definition is,
This will form a geometric sequence with first term 4.5 and common ratio r=-6.
When n=2, we have:
When n=3, we get:
When n=4, we get:
When n=5, we get:
Therefore the first five terms are:
4.5, -27, 162,-972, 5832
The equation that matches the given table is
y = 10x + 40
Solution:
General equation of a line : y = mx + c
Let us find the equation of the table.
<u>Common differences of X: </u>
0 – 1 = 1, 1 – 2 = 1, 3 – 2 = 1, 4 – 3 = 1, 5 – 4 = 1
<u>Common differences of Y: </u>
50 – 40 = 10, 60 – 50 = 10, 70 – 60 = 10, 80 – 70 = 10, 90 – 80 = 10
m = 10
Substitute m = 10 in general equation of a line
y = 10x + c
To find the constant term, substitute x = 0 and y = 40.
40 = 10(0) + c
40 = 0 + c
40 = c
c = 40
Therefore the equation of a line is y = 10x + 40.
Hence the equation that matches the given table is y = 10x + 40.