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 29th in an arithmetic progression if the sum of the 13th and 17th terms of the sequence is 102?
Choose the correct choice from the following answers:
A) 43
B) 47
C) 51
D) 55
E) 59
Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 15th term in the sequence.   Then the mean of the 14th and 16th term is also equal to the overall mean, because the 14th term is (15th term - x) and the 16th term is (15th term + x).   Similarly the mean of the 13th and 17th term is also equal to the mean.   etc...   Thus the mean is   102/2= 
<gadget id="calculator">  102/2</gadget>
<output>51</output>
51   The answer is 51.
<result>C</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 29th in an arithmetic progression if the sum of the 13th and 17th terms of the sequence is 102?