Respuesta :
Answer:
[tex]a_{n}[/tex] = 3n - 1
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 5 - 2 = 8 - 5 = 11 - 8 = 14 - 11 = 3
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 3 , thus
[tex]a_{n}[/tex] = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1
The expression for the nth term of the series is [tex]a_n = 3n-1[/tex].
Given that,
Sequence; 2, 5, 8, 11, 14.
We have to find, the expression in terms of n for the nth term of the following given sequences?
According to the question,
The nth of the arithmetic sequence is,
[tex]\rm a_n = a+ d(n-1)[/tex]
Where a is the first term of the sequence,
d is the common difference between the terms,
n is the number of terms.
Then,
The given sequence is 2, 5, 8, 11, 14.
Here, the common difference between the terms is 3.
And the first term of the sequence is 2.
Substitute all the values in the formula,
Therefore,
The nth term of the given terms is,
[tex]\rm a_n = a+ d(n-1)\\\\a_n = 2+ 3(n-1)\\\\a_n + 2+3n-1\\\\a_n = 3n-1[/tex]
Hence, The required expression for the nth term of the series is [tex]a_n = 3n-1[/tex].
For more details refer to the link given below.
https://brainly.com/question/17043393
