Multiple choice

Observe the following sequence. What is the $100^{th}$ term? $7, 8, 1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 3,...$

  1. $1$
  2. $0$
  3. $2$
  4. $3$
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A Correct answer
AI explanation

The sequence is derived from the decimal digits of the square roots of consecutive integers starting from 2. The 100th term corresponds to the 100th digit overall, which falls within the expansion of the square root of 11. The decimal expansion of sqrt(11) is 3.3166247903..., and the required digit is exactly 1.

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