SOLUTION: Insert 6 arithmetic means between 12 and 75

Algebra ->  Sequences-and-series -> SOLUTION: Insert 6 arithmetic means between 12 and 75      Log On


   

Question 1091303: Insert 6 arithmetic means between 12 and 75
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We are to fill the 6 blanks below so that the sequence

12, __, __, __, __, __, __, __, 75

of 8 terms is an arithmetic sequence. We use
the formula:

a%5Bn%5D%22%22=%22%22a%5B1%5D%2B%28n-1%29d

using a1=12, n=8, a8=75

a%5B8%5D%22%22=%22%2212%2B%288-1%29d

75%22%22=%22%2212%2B%288-1%29d 

75%22%22=%22%2212%2B7d

63%22%22=%22%227d

63%2F7%22%22=%22%227d%2F7

9%22%22=%22%22d

So we add 9 six times, starting by adding it
to 12, and the 6 arithmetic means are the 6
underlined numbers below:

12, 21, 30, 39, 48, 57, 66, 75

and as a check, when we add 9 to the last one, 66, we do get 75.

Edwin