Question

Find the common difference of the arithmetic sequence given that a5 = 58 and a12 = 149.

Answer 1

http://www.mathsisfun.com/definitions/common-difference.html
Example: the series {3, 5, 7, 9, 11, ...} is made by adding 2 each time, and so has a "common difference" of 2 (there is a difference of 2 between each number)


So in the above example, where
a1=3
a2=5
a3=7
a4=9
a5=11
...
a12=25

a12-a5= 7 jumps

a12 (25) minus a5 (11) equals 14. 14 divided by the # of jumps (7) = 2

Therefore the common difference is 2. Now in this case we already knew the number of jumps beforehand, so we know we have the right answer. Applying the same idea to your problem:

a12-a5= 7 jumps

a12 (149) minus a5 (58) equals 91. 91 divided by the number of jumps (7) = 13