The average of five consecutive natural numbers is 13. If the next two natural numbers are also included, then find the new average.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 14
The average of an odd number of consecutive numbers is the middle number, because the numbers on either side of it balance out.
Five consecutive numbers with average 13: 11, 12, 13, 14, 15 (sum 65)
The next two numbers: 16 and 17
New sum \(=65+16+17=98\)
New average \(\displaystyle =\frac{98}{7}=14\)
Shortcut: The seven numbers 11 to 17 are again consecutive, so their average is the middle number, the 4th of them: 14.