Answer:
a(1) = 2
a(n) = a(n-1)+4
Step-by-step explanation:
Using the given arithmetic sequence,
a1 is 2
a2 is 6
a3 is 10
a4 is 14
a5 is 18
and to get from a1 to a2 you have to +4, to get from a2 to a3 you have to +4 and so on.
In a reclusive formula you need to find two pieces of information:
1. The first term of the sequence
2. The pattern rule to get any term from the term that comes before it
Using the given sequence, the first term is 2 and the rule to get any term from its previous term is +4.
So, putting that information in the form of a recursive formula will read as the following:
an+1 = an+4
a1 = 2, n is greater or equal to 1 (n is an interger)
Which can be rearranged to
a(1) = 2
a(n) = a(n-1)+4
