Respuesta :
Answer:
- 90
Step-by-step explanation:
These are the terms of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
d = 6 - 9 = 3 - 6 = - 3 and a = 9, hence
[tex]a_{34}[/tex] = 9 - 3 × 33 = 9 - 99 = - 90
The [tex]a_{34}[/tex] is -90 in the given sequence.
The given sequence is 9,6,3,......
We are asked to find the [tex]34^{th}[/tex] term in the sequence which is denoted by [tex]a_{34}[/tex].
We first need to know what type of sequence is given in the question.
What is an arithmetic sequence?
A sequence where the difference between the consecutive terms is always the same.
The formula used to find the value of the required term is given by:
[tex]a_n = a + (n-1)d[/tex]
Where a = first term, n = the term value and d = common difference.
The given sequence is 9,6,3,.....
We see that the given sequence is an arithmetic sequence.
6 - 9 = -3 and 3 - 6 = -3
so,
d = -3.
Here a = 9.
And we need to find the value in the sequence at n = 34.
substituting a,d, and n values in [tex]a_n = a + (n-1)d[/tex].
We get,
[tex]a_{34} = 9 + ( 34 - 1 ) (-3)\\a_{34} = 9 + 33(-3)\\a_{34} = 9 - 99\\a_{34} = -90[/tex]
Thus, the [tex]a_{34}[/tex] is -90 in the given sequence.
Learn more about arithmetic sequence here:
https://brainly.com/question/12974193
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