Respuesta :
The explicit formula for the arithmetic sequence. 3, -3, -9, -15, -21, ...
is (9 - 6n).
The given arithmetic sequence is 3, -3, -9, -15, -21, ...
We have to find the explicit formula to find the nth term (any term) in the sequence.
What is an arithmetic sequence?
A sequence where between two consecutive numbers the difference is the same.
d = common difference.
a = first value in the sequence.
the nth term in an arithmetic sequence is given by:
[tex]a_{n}[/tex] = a + ( n - 1 ) d
We have,
3, -3, -9, -15, -21, ...
a = 3
Find the common difference.
d = -3 - 3 = -6
d = -9 - (-3) = -9 + 3 = -6
d = -15 - (-9) = -15 + 9 = -6
We see that d = -6.
So the explicit formula for the given arithmetic sequence is:
[tex]a_{n}[/tex] = a + ( n - 1 ) d
= 3 + ( n - 1 ) (-6)
= 3 + ( -6n - 1 x -6 )
= 3 + ( -6n + 6 )
= 3 - 6n + 6
= 9 - 6n
Thus the explicit formula for the arithmetic sequence. 3, -3, -9, -15, -21, ...
is (9 - 6n).
Learn more about arithmetic sequence here:
https://brainly.com/question/13881016
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