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 27th in an arithmetic progression if the sum of the 12th and 16th terms of the sequence is 98?
Select the correct option
A) 47 B) 49 C) 51 D) 53 E) 55
Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 14th term in the sequence.   Then the mean of the 13th and 15th term is also equal to the overall mean, because the 13th term is (14th term - x) and the 15th term is (14th term + x).   Similarly the mean of the 12th and 16th term is also equal to the mean.   etc...   Thus the mean is   98/2= 
<gadget id="calculator">  98/2</gadget>
<output>49</output>
49   The answer is 49.
<result>B</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 27th in an arithmetic progression if the sum of the 12th and 16th terms of the sequence is 98?