题目

Problem

An arithmetic progression has fourth term 15 and eighth term 25.

Find the 30th term of the progression.

[3]

题目中文翻译

一个等差数列的第 4 项为 15，第 8 项为 25。

求该数列的第 30 项。

解答

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从第 $4$ 项到第 $8$ 项经过四个公差，先求出公差，再从第 $8$ 项数到第 $30$ 项。

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The common difference is $d=(25-15)/(8-4)=\frac52$ . There are $30-8=22$ steps after the eighth term, so the 30th term is

25+22\cdot\frac52=80.