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 33rd in an arithmetic progression if the sum of the 15th and 19th terms of the sequence is 108?  Select
A) 38 B) 42 C) 46 D) 50 E) 54
Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 17th term in the sequence.   Then the mean of the 16th and 18th term is also equal to the overall mean, because the 16th term is (17th term - x) and the 18th term is (17th term + x).   Similarly the mean of the 15th and 19th term is also equal to the mean.   etc...   Thus the mean is   108/2= 
<gadget id="calculator">  108/2</gadget>
<output>54</output>
54   The answer is 54.
<result>E</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 33rd in an arithmetic progression if the sum of the 15th and 19th terms of the sequence is 108?