Question

Which answer is the explicit rule for the sequence 3, 8, 13, 18, 23 ... ?

an=−2+3n
an=−2+5n
an=−2−5n
an=2+5n

Answer 1

The answer would be an=-2+5n

Answer 2

B.
`a_n=-2+5n`

Explanation:

We have been given a sequence. We are asked to find the explicit rule for the given sequence.

3, 8, 13, 18, 23 ...

We know that explicit formula for a sequence is
`a_n=a_1+(n-1)d`, where,

`a_n` = nth term of the sequence,

`a_1` = 1st term of the sequence,

`d` = common difference.

Upon looking at our given sequence we can see that
`a_1=3`.

Let us find common difference between two terms by subtracting 3 from 8 as:

`d=8-3=5`

Upon substituting these values in explicit formula we will get,

`a_n=3+(n-1)5`

`a_n=3+5n-5`

`a_n=-2+5n`

Therefore, option B is the correct choice.