Question

Please help me with this

Answer 1

Answer:
`a_(n)=4n+-3`

Explanation:

The way arithmetic sequences are usually written is:

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

`a_(n)` is the the term you are looking for. It has an n because we aren't looking for a specific one.

`a_(1)` is the first term of the sequence. In this case that is 1.

n is the term position. Meaning if you wanted to find the fifth term you'd sub 5 in for n.

d is the common difference. In this case it is 4.

Now we can sub these values in.

`a_(n) =1 +(n-1)4`

We can simplify the right part of the equation.

`a_(n) =1 +(n-1)4\\a_(n) =1 +(4)(n)-(4)(1)\\a_(n)=1+4n-4\\a_(n)=4n+1-4\\a_(n)=4n+-3`