Question

Can you help find the first 5 terms and the explicit formula

Answer 1

Remember that the explicit formula for an arithmetic sequence is:

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

`a_(n)` is the nth term

`a_(1)` is the first term

`n` is the position of the term in the sequence

`d` is the common difference

We know from our problem that
`a_(1)=7` and
`d=7`, so lets replace those vales in our formula:

`a_(n)=7+(n-1)7`

`a_(n)=7+7n-7`

`a_(n)=7n`
Now that we have the explicit formula for our sequence we can find its first 5 terms:

`a_(1)=7`

`a_(2)=7(2)=14`

`a_(3)=7(3)=21`

`a_(4)=7(4)=28`

`a_(5)=7(5)=35`

We can conclude that the first five terms of our arithmetic are: 7,14,21,28,35, and its explicit formula is
`a_(n)=7n`