There are 32 consecutive natural numbers. The average of the first 13 numbers is x. What is the average of the next 19 numbers?
Answer & explanation
Correct answer: option 2
Sum of first 32 consecutive numbers = \(\frac{n(n+1)}{2}\)
= \(\frac{32 × 33}{2}\) = 528
Average of first 13 numbers = \(\frac(n+1)}{2}\) = \(\frac{14}{2}\) = 7
so x = 7
Sum of 13 numbers = 13 × 7 = 91
Remaining sum of 19 numbers = 528 - 91 = 437
Average of 19 numbers = \(\frac{437}{19}\) = 23
23 = 7 + 17 = x + 16
SO , ans is x + 16