SOLUTION: The sum of first 3 integers in an Arithmetic progression is 36. The sum of the next 3 integers is 72. What is the common difference between the terms?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The sum of first 3 integers in an Arithmetic progression is 36. The sum of the next 3 integers is 72. What is the common difference between the terms?      Log On


   

Question 1124696: The sum of first 3 integers in an Arithmetic progression is 36. The sum of the next 3 integers is 72. What is the common difference between the terms?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

(1) +a%5B1%5D+%2B+%28a%5B1%5D%2Bd%29+%2B+%28a%5B1%5D%2B2d%29+=+36+
(2) +%28a%5B1%5D%2B3d%29+%2B+%28a%5B1%5D%2B4d%29+%2B+%28a%5B1%5D%2B5d%29+=+72+
(1) ==> 3a%5B1%5D+%2B+3d+=+36+
(2) ==> 3a%5B1%5D+%2B+12d+=+72+
Subtract (1) from (2):
+9d+=+36+ —> +highlight%28+d+=+4+%29+
————————
Another approach:
In the first group of three, the average value is 36/3 = 12 (= middle value, a%5B2%5D )
In the 2nd group of three, the average value is 72/3 = 24 (= middle value, a%5B5%5D )
Since +a%5B5%5D+=+a%5B2%5D+%2B+3d+: 24 = 12 + 3d —> 3d = 12 —> d = 4