Sequences & Series
Triangular Array — Row of a Number
nta_pyq_2024_apr
Grade 11
Question:
Let the positive integers be written in the form: Row 1: 1; Row 2: 2,3; Row 3: 4,5,6; Row 4: 7,8,9,10; $\ldots$ If the $k$th row contains exactly $k$ numbers for every natural number $k$, then the row in which the number 5310 will be, is
Step-by-Step Solution
Key Concept: The last number in row $k$ is $1+2+\cdots+k=k(k+1)/2$. Find $k$ such that $k(k+1)/2\geq5310$.
5310 is in row 103.
Correct Answer: 103