Question

Consider this sequence:

Answer 1

nth term is: $a_n=6n-2$

122 is not in the sequence

Further explanation:

First of all we have to decide whether it an arithmetic sequence or geometric sequence,

Here

$a_1=4\\a_2=10\\a_3=16\\a_4=22\\d=a_2-a_1\\=10-4\\= 6$

$a_3-a_2=16-10=6$

As the common difference is same for all consecutive terms, the sequence is an arithmetic sequence

The formula for arithmetic sequence is given by:

$a_n=a_1+(n-1)d$

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

$a_n=4+(n-1)(6)\\a_n=4+6n-6\\=6n-2$

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,

$122=6n-2\\Adding\ 2\ on\ both\ sides\\122+2=6n-2+2\\124=6n\\Dividing\ both\ sides\ by\ 6\\\frac{6n}{6}=\frac{124}{6}\\n=20.6666$

As the value of n is in decimal, that means none of the terms in the sequence is 122.

So,

nth term is: $a_n=6n-2$

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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