What is in the 150th position of 1234 12344 123444 1234444 .............. ?
2026
What is in the 150th position of 1234 12344 123444 1234444 .............. ?
- A.
3
- B.
4
- C.
5
- D.
6
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Show answer & explanation
Correct answer: A
Answer: 3
Sequence description: Each group k is the digits 1, 2, 3 followed by k copies of 4, so the length of group k is 3 + k.
Total digits in the first n groups = sum_{k=1..n} (3 + k) = 3n + n(n+1)/2 = (n^2 + 7n)/2.
Find n such that (n^2 + 7n)/2 ≥ 150. Solving n^2 + 7n - 300 ≥ 0 gives the positive root ≈ 14.17, so the smallest integer n with total ≥ 150 is n = 15. Thus the 150th digit is in group 15.
Total digits up to group 14 = (14^2 + 7·14)/2 = 147. Therefore digits 148, 149, 150 are the first three digits of group 15, namely 1, 2, 3.
Hence the 150th digit is 3.