The correct answer is C) 1, 4, 9, 16, 25,
The sequence {Fₙ} is defined as the largest integer k such that k² ≤ n. Let's analyze each given sequence to determine which one fits this definition:
A) 1, 1, 1, 2, 2,...
The square of the terms in this sequence are 1, 1, 1, 4, 4,... The largest integer k such that k² ≤ n is the integer part of the square root of n. Therefore, the sequence doesn't fit the definition, as the terms do not represent the largest integer whose square is less than or equal to n.
B) 2, 4, 8, 16, 32,...
The square of the terms in this sequence are 4, 16, 64, 256, 1024,... The largest integer k such that k² ≤ n is the integer part of the square root of n. Therefore, this sequence does not fit the definition.
C) 1, 4, 9, 16, 25,...
The square of the terms in this sequence are 1, 16, 81, 256, 625,... The largest integer k such that k² ≤ n is the integer part of the square root of n. This sequence fits the definition, as each term represents the largest integer whose square is less than or equal to n.
Therefore, the correct answer is C) 1, 4, 9, 16, 25,...