Write a rule for the nth term of the arithmetic sequence.

a14 = 42, d=3

So the rule for the nth term is:

an = 3 + (n - 1) * 3

Step-by-step explanation:

On an arithmetic sequence each element is related to it's neighbors by the sum of a ratio, in this case "3". The "nth" term or general term of a sequence of this kind is given by:

an = a1 + (n - 1) * d

Where an is the nth term, a1 is the first term, n is the number of the term in the sequence and d is the ratio. Therefore we need to first find a1 to write the rule. Applying the data from the problem we can solve for a1, we have:

42 = a1 + (14 - 1) * 3

42 = a1 + (13) * 3

42 = a1 + 39

a1 = 42 - 39 = 3

So the rule for the nth term is:

an = 3 + (n - 1) * 3