Question

Generalize the pattern by finding the nth term.

6, 10, 14, 18, ....

Question 1 options:

2n + 4


4n + 2


4n + 6

Answer 1

4n+2

Explanation:

The common difference between the terms is 4 which means that the sequence is an arithmetic sequence.

The general formula for arithmetic sequence is:

`a_(n)=a_(0)+(n-1)d`

where a_n is the nth term, a_0 is the first term and d is the common difference between them.

We know that

`a_(0)=6\\d=4`

Putting the value in general formula:

`a_(n)=6+4(n-1)\\a_(n)=6+4n-4\\a_(n)=4n+6-4\\a_(n)=4n+2\\`

So the generalized pattern is 4n+2 ..