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2026 AMC 10A Problem 18

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2026 AMC 10A Problem 18AMC 10 Step by Step

Name: Date: November 10, 2026

Sequences & Series · difficulty 3 of 5 · about 4 min · position P16-20

The strictly decreasing sequence of $11$ positive integers $(a_0,a_1,a_2,…,a_{10})$ is defined by the recursive rule $a_k=\frac{1}{2}a_{k-1}+2$ , for $k \geq 1$ . Let $N$ be the minimum possible value of $a_0$ . What is the sum of the digits of $N$ ?

A) $8$
B) $9$
C) $10$
D) $11$
E) $12$

2026 AMC 10A Problem 18

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