What function forms a geometric sequence when x= 1,2,3,....?
2 answers:
the second function is a geometric sequence
the first function is an arithmetic sequence
the third and fourth are constants
For a sequence to be geometric it must have a common ratio r between the terms
the n th term of a geometric sequence is a
where a is the first term and r the common ratio
f(x) = - 5 is in this form with r = 3
As a check
f(1) = - 5 × 3 = - 15
f(2) = - 5 × 9 = - 45
f(3) = - 5 × 27 = - 135
This is a geometric sequence with r = 3
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A
this is an arithmetic sequence whose n th term ( explicit formula) is
=
+ (n - 1 )d
where d is the common difference and the first term
here d = 10 - 8 = 8 - 6 = 6 - 4 = 2 and = 4, hence
= 4 + 2(n - 1 ) = 4 + 2n - 2 = 2n + 2 → A
The lines whose equation is x = a, are vertical lines that pass through the point (a, y) where y is any real number. Additionally, vertical lines have an indefinite slope.
You can see it in the graph of this equation:
