INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

June 22, 2020

Missing Integers | PRMO II 2019 | Question 1

Try this beautiful problem from the PRMO II, 2019 based on Missing Integers.

Missing Integers - PRMO II 2019

Consider the sequence of numbers [n+\(\sqrt{2n}+\frac{1}{2}\)] for \(n \geq 1\), where [x] denotes the greatest integer not exceeding x. If the missing integers in the sequence are \(n_1<n_2<n_3<...\) then find \(n_{12}\).

  • is 107
  • is 78
  • is 840
  • cannot be determined from the given information

Key Concepts

Real Numbers



Check the Answer

Answer: is 78.

PRMO II, 2019, Question 1

Elementary Algebra by Hall and Knight

Try with Hints

First hint


Let P=[\((\sqrt{n}+0.7)^2\)]

Second Hint

given \(n \geq 1\), put n=1 gives P=2

n=2 gives P=4

n=3 gives P=5

n=4 gives P=7

n-5 gives P=8

n=6 gives P=9

n=7 gives P=11

Final Step

here missing number are

1,3,6,10,... which is following a certain pattern

1, 1+2, 3+3, 6+4, 10+5, 15+6, 21+7, 28+8, 36+9, 45+10, 55+11, 66+12.

so, \(n_{12}\)=78.

Subscribe to Cheenta at Youtube

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.