Question

Consecutive natural numbers starting from 1 are written on a blackboard. A student erases 3 consecutive numbers of the series. The average now becomes 414/19. What is the average of the erased numbers?

Answer 1

Answer:

Step-by-step explanation:

Let the total number of numbers initially were N. Then

N=19K+3

The sum of first N natural numbers is given by N(N+1)2. Putting above in the expression, sum of N natural numbers S would be:

S=(19K+3)(19K+4)2

Let the three removed numbers be P-1, P and P+1. Now calculating the average we can come up with the equation:

(19K+3)(19K+4)2−3P19K=41419

Rearranging,  

P=361K2−695K+126

Putting K=2 gives P=11, which is our answer.

The total numbers of initial numbers comes out as 19K+3=41 with a sum of 861, and after the removal of 10, 11 and 12, the sum becomes 828 and they average out as 828/38.