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China Mathematical Competition

Algebra Difficulty 3.8 AMC 10/12 Find the answer China

Given arithmetic sequence $\{a_n\}$ with common difference $d \ne 0$ and $a_{2021} = a_{20} + a_{21}$ , then the value of $\frac{a_1}{d}$ is ______.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

By the conditions, we have $a_1 + 2020d = a_1 + 19d + a_1 + 20d$ . And since $d \ne 0$ , $\frac{a_1}{d} = 1981$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.