Respuesta :
Answer:
[tex]a_n = a_{n-1}-13.8[/tex]
Step-by-step explanation:
The recursive rule for the arithmetic sequence is given by:
[tex]a_n = a_{n-1}+d[/tex] .....[1]
where, d is the common difference of two consecutive terms.
Given the sequence:
−7.4, −21.2, −35, −48.8, −62.6
This is an arithmetic sequence
Here, first term[tex](a_1)[/tex] = -7.4 and d = -13.8
Since,
-21.2+7.4 = -13.8,
-35+21.2 = -13.8 ans so on...
Substitute the given value in [1] we have;
[tex]a_n = a_{n-1}+(-13.8)[/tex]
⇒[tex]a_n = a_{n-1}-13.8[/tex]
Therefore, the recursive rule for the sequence is, [tex]a_n = a_{n-1}-13.8[/tex] and [tex]a_1[/tex]= -7.4
The recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex] and [tex]\rm a_{1}[/tex] = -7.4.
What is the recursive rule?
The recursive rule refers to the first term of the sequence and describe
the relation to the preceding term with the recursive equation.
The recursive formula for the arithmetic sequence is as follows
[tex]\rm a_{n} = a_{n-1} + d[/tex]
where [tex]\rm a_{n}[/tex] is the nth term and d is a common difference
The arithmetic sequence is given as
−7.4, −21.2, −35, −48.8, −62.6
[tex]\rm a_{1}[/tex] = -7.4 (first term)
d = -21.2+7.4 = -13.8,
d = -35+21.2 = -13.8
Substitute the given value, we get
[tex]\rm a_{n} = a_{n-1} + d[/tex]
[tex]\rm a_{n} = a_{n-1} -13.8[/tex]
Hence, the recursive rule for the sequence is [tex]\rm a_{n} = a_{n-1} -13.8[/tex] and [tex]\rm a_{1}[/tex] = -7.4.
Learn more about the recursive rule:
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