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# Algebra

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The numbers 2,4,x form a geometric progression and the sequence 3,x,y is an arithmetic progression. Determine the value of y.

Jun 17, 2022

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Note that if three numbers x, y, z form an arithmetic progression, then $$y = \dfrac{x + z}2$$.

Also, if three numbers a, b, c form a geometric progression, then $$b^2 = ac$$.

Therefore, $$4^2 = 2\cdot x$$. Solving gives x = 8.

Can you continue from here?

Jun 18, 2022