In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 31st in an arithmetic progression if the sum of the 14th and 18th terms of the sequence is 122?	Choose the correct choice from the following choices.
A) 46  B) 51  C) 56  D) 61  E) 66
Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 16th term in the sequence.   Then the mean of the 15th and 17th term is also equal to the overall mean, because the 15th term is (16th term - x) and the 17th term is (16th term + x).   Similarly the mean of the 14th and 18th term is also equal to the mean.   etc...   Thus the mean is   122/2= 
<gadget id="calculator">  122/2</gadget>
<output>61</output>
61   The answer is 61.
<result>D</result>
In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 31st in an arithmetic progression if the sum of the 14th and 18th terms of the sequence is 122?