HMMT February

Algebra Difficulty 4.7 AIME Find the answer

When a single number is added to each member of the sequence 20, 50, 100, the sequence becomes expressible as $x, a x, a^{2} x$ . Find $a$ .

Your answer

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

Solution

$\frac{5}{3}$ .

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Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.