A recursive rule for an arithmetic sequence is a1 = 4; an = an-1 + 3 . What is an explicit rule for this sequence? (Picture attached) please help? I don't remember what type of equation to use for these kinds of problems...
Accepted Solution
A:
Answer: 3n+1 (no need to type in the "a_n" or "an" part, as it's already done)
The first term is a1 = 4 since it is given to us The common difference is d = 3. This is the value that we add to each term to get the next as the recursive steps shows when we write a(n) = a(n-1)+3 In other words, nth term = [ (n-1)st term ] + 3 next term = (previous term) + 3
Using a1 = 4 and d = 3, we get the following an = a1+d(n-1) an = 4 + 3(n-1) an = 4+3n-3 an = 3n + (4-3) an = 3n+1