Respuesta :
Answer:
no
Step-by-step explanation:
Establish the nth term formula
There is a common difference d between consecutive terms, that is
d = - 5 - (- 9) = - 1 - (- 5) = 3 - (- 1) = 7 - 3 = 4
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 9 and d = 4 , then
[tex]a_{n}[/tex] = - 9 + 4(n - 1) = - 9 + 4n - 4 = 4n - 13
Equate 4n - 13 to 301
4n - 13 = 301 ( add 13 to both sides )
4n = 314 ( divide both sides by 4 )
n = 78.5
Since n is not an integer then 301 is not in the sequence
301 doesn't belong to the sequence -9, -5,-1,3,7,...
What is A.P sequence?
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The arithmetic sequence is given by a, a + d, a + 2d, a + 3d, … .
Hence, the formula to find the nth term is:
[tex]a_{n}[/tex] = a + (n – 1) × d.
where,
a = first term
d = common difference
n = number of terms
[tex]a_{n}[/tex] = nth term
According to the question
Sequence : -9, -5,-1,3,7,...
First term (a)= -9
common difference (d)= -5 - (-9)
= 4
[tex]a_{n}[/tex] = 301
using the formula of nth term
[tex]a_{n}[/tex] = a + (n-1)d
Substituting the value
301 = -9 + (n-1) 4
310 = (n-1) 4
77.5 = (n-1)
n = 78.5
as n always to be the whole number .
Hence, 301 doesn't belong to the sequence -9, -5,-1,3,7,...
To know more about A.P sequence here:
https://brainly.com/question/24205483
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