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Consider the arithmetic sequence in which a1=6  and a14=97.

a. Determine the rule for the sequence, and explain your reasoning.

 Jan 2, 2021
 #1
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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.

 Jan 3, 2021

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