Pre-calculus

Question

An arithmetic sequence has a 10th term of 17 and a 14th term of 30. Find the common difference.

Answer 1

Since we add the same amount every time (common difference), to get from the 10th term to the 14th, we would have added the common difference 4 times.  The overall difference between 30 and 17 is 13, divided into 4 pieces gives us a common difference of 3.25.

 

This is pretty much the same concept as finding the slope of a line where you take the difference of the y's and divide by the difference of the x's.