Consider the arithmetic sequence in which a1=6 and a14=97.
a. Determine the rule for the sequence, and explain your reasoning.
97 = 6 + 13 D, solve for D
D = 7 - this is the common difference
So, your sequence begins like this:
6, 13, 20, 27, 34, 41..........and so on. Just add 7 to each term after the first.
The rule is: a(n) =7n - 1 . The rule is very simple. Just sub 1, 2, 3, 4, 5.......etc. for n and you get the term that you want.