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The average of seven consecutive natural numbers is 13. If the next three consecutive natural numbers are also included, the new average will be
Explanation
For any sequence of n consecutive natural numbers, the average is the middle term (if n is odd) or the arithmetic mean of the two middle terms (if n is even). It can also be calculated as (First Term + Last Term) / 2.
Given the average of 7 consecutive numbers is 13, the middle (4th) term is 13. The sequence is: 10, 11, 12, 13, 14, 15, 16.
When the next three consecutive natural numbers (17, 18, and 19) are included, the new sequence becomes: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
New Average = (First Term + Last Term) / 2 = (10 + 19) / 2 = 29 / 2 = 14.5.
Short Trick: If m subsequent consecutive numbers are added to an existing series of consecutive numbers, the average increases by m/2. Here, m = 3, so the increase is 3/2 = 1.5. New average = 13 + 1.5 = 14.5.