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The phrase "a first reason is" is correct and usable in written English.
It can be used when introducing the first point or argument in a discussion or explanation.
Example: "A first reason is that regular exercise improves mental health and reduces stress."
Alternatives: "The initial reason is" or "One reason is".
Exact(3)
A first reason is that it is more important than regional liberalization such as NAFTA.
A first reason is that acquiring the spectral reflectance is the most reliable asset for faithful color reproduction, where faithfulness is measured in terms of independence from illumination and acquisition devices.
A first reason is that the relationship between the decision to implement an intervention, the actual implementation and assessment of intervention outcomes is not linear but cyclical, as ex post assessment of an intervention will feed into ex ante assessment to support the decision on whether an intervention should be continued in its current form, continued with adjustments, or discontinued.
Similar(57)
A second reason is sustainability.
A third reason is education.
A second reason is globalization.
A second reason is the rat race.
A third reason is credibility.
A second reason is free speech.
A second reason is a love of killing things.
A second reason is the symbolism of the moment.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com