Jerry wrote down the ones digit of each of the first $2025$ positive squares: $1, 4, 9, 6, 5, 6, \dots$. What is the sum of all the numbers Jerry wrote down?
$$\textbf{(A) } 9025 \qquad \textbf{(B) } 9070 \qquad \textbf{(C) } 9090 \qquad \textbf{(D) } 9115 \qquad \textbf{(E) } 9160$$
Difficulty: 19/100 — A somewhat challenging problem for beginners which can become computation heavy.
Core Concepts: pattern recognition, arithmetic, cycles
Challenges: Figuring out how to compute the sum once you figure out the sequence's repetition.
Techniques: Work through first terms and scan for repetition.
Error-prone Steps: Computation mistakes.
Ideal Time:
Experienced: ≤ 1 min
Intermediate: ≤ 2 min
Beginner: ≤ 4 min