nth term is: [tex]a_n=6n-2[/tex]
122 is not in the sequence
Further explanation:
First of all we have to decide whether it an arithmetic sequence or geometric sequence,
Here
[tex]a_1=4\\a_2=10\\a_3=16\\a_4=22\\d=a_2-a_1\\=10-4\\= 6[/tex]
[tex]a_3-a_2=16-10=6[/tex]
As the common difference is same for all consecutive terms, the sequence is an arithmetic sequence
The formula for arithmetic sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]
Here a_n is the nth term
a1 is the first term
n is the term number and
d is the common difference
Putting the value of a1=4 and d=6 in the formula
[tex]a_n=4+(n-1)(6)\\a_n=4+6n-6\\=6n-2[/tex]
To check whether 122 will be number in the sequence or not,
Putting the value in nth term we will find the value of n, if n is an integer then 122 is a part of the sequence, otherwise not
So,
[tex]122=6n-2\\Adding\ 2\ on\ both\ sides\\122+2=6n-2+2\\124=6n\\Dividing\ both\ sides\ by\ 6\\\frac{6n}{6}=\frac{124}{6}\\n=20.6666[/tex]
As the value of n is in decimal, that means none of the terms in the sequence is 122.
So,
nth term is: [tex]a_n=6n-2[/tex]
122 is not in the sequence
Keywords: Arithmetic sequence, Common Difference
Learn more about arithmetic sequence at:
- brainly.com/question/13219835
- brainly.com/question/1836777
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