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 25th in an arithmetic progression if the sum of the 11th and 15th terms of the sequence is 96? Select.
A) 48  B) 63  C) 55  D) 96  E) 108
Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 13th term in the sequence.   Then the mean of the 12th and 14th term is also equal to the overall mean, because the 12th term is (13th term - x) and the 14th term is (13th term + x).   Similarly the mean of the 11th and 15th term is also equal to the mean.   etc...   Thus the mean is   96/2= 
<gadget id="calculator">  96/2</gadget>
<output>48</output>
48   The answer is 48.
<result>A</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 25th in an arithmetic progression if the sum of the 11th and 15th terms of the sequence is 96?