What is a2-a1 : b3-b1 in this AP?

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X  a1  a2  Y
X b1 b2 b3 Y

what is a2-a1 : b3-b1 in this AP? i was getting an answer of 2/3. don't know if it's correct.

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Your answer is correct.

$a_2 - a_1 = \frac{1}{3} (Y-X)$ and $b_3 - b_1 = \frac{1}{2} (Y-X) $.