Answer:
B. [tex]a_n=-2+5n[/tex]
Step-by-step 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 [tex]a_n=a_1+(n-1)d[/tex], where,
[tex]a_n[/tex] = nth term of the sequence,
[tex]a_1[/tex] = 1st term of the sequence,
[tex]d[/tex] = common difference.
Upon looking at our given sequence we can see that [tex]a_1=3[/tex].
Let us find common difference between two terms by subtracting 3 from 8 as:
[tex]d=8-3=5[/tex]
Upon substituting these values in explicit formula we will get,
[tex]a_n=3+(n-1)5[/tex]
[tex]a_n=3+5n-5[/tex]
[tex]a_n=-2+5n[/tex]
Therefore, option B is the correct choice.
