The average of seven consecutive natural numbers is 13. If the next three consecutive natural numbers are also included, the new average will be
15.0
14.5
13.5
13.0
Answer is Right!
Answer is Wrong!
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UPSC CISF-AC-EXE – 2024
In an arithmetic progression (which consecutive natural numbers are), the average is equal to the middle term.
For 7 consecutive numbers, the middle term is the 4th number.
So, the 4th number is 13.
Let the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. The 4th number is $n+3$.
$n+3 = 13 \implies n = 10$.
The seven consecutive natural numbers are 10, 11, 12, 13, 14, 15, 16.
The sum of these 7 numbers is $7 \times 13 = 91$.
The next three consecutive natural numbers are 17, 18, 19.
When these three numbers are included, the new set of numbers is 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. There are now 10 numbers.
The sum of the new set of numbers = Sum of original 7 numbers + Sum of next 3 numbers.
Sum of next 3 numbers = 17 + 18 + 19 = 54.
Total sum of 10 numbers = 91 + 54 = 145.
The new average = Total sum / Number of terms = 145 / 10 = 14.5.