Question

32. The positive integers are in form of triangle as shown

1 2 3 4 5 6 7 8 9 10 ... ... ... then row in which the number 100 will be

• A. 15
• B. 20
• C. 14
• D. 22

Answer 1

Answer: (C)

14

Answer 2

The last number in row 'n' of the triangular arrangement is given by the sum of the first 'n' natural numbers, $L_n = \frac{n(n+1)}{2}$. We need to find the row 'n' where the number 100 lies.

For $n=13$, $L_{13} = \frac{13 \times 14}{2} = 91$. This means row 13 ends with 91.

For $n=14$, $L_{14} = \frac{14 \times 15}{2} = 105$. This means row 14 ends with 105.

Since the number 100 is greater than 91 and less than or equal to 105, it must be in row 14.