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Algebra Difficulty 1.4 Junior Find the answer Canada

The numbers $4x, 2x-3, 4x-3$ are three consecutive terms in an arithmetic sequence. What is the value of $x$ ?

(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, $3, 5, 7, 9$ are the first four terms of an arithmetic sequence.)

Pick one

Solution

Since $4x,2x-3,4x-3$ form an arithmetic sequence, then the differences between consecutive terms are equal, or $(2x-3) - 4x = (4x-3)-(2x-3)$ .

Thus, $-2x - 3 = 2x$ or $4x = -3$ and so $x = - \frac{3}{4}$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.