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The phrase "and the first model" is correct and usable in written English.
It can be used when referring to a specific model in a sequence or comparison, often in contexts like discussions about prototypes, designs, or examples.
Example: "We have several prototypes, and the first model was the most successful in testing."
Alternatives: "as well as the initial model" or "along with the primary model".
Exact(14)
UNIVAC, the first commercial computer in the U.S., was developed by ENIAC's inventors, and the first model sold went to the Census Bureau.
It is creating its new line of phones under the Xperia brand, and the first model, the top of that line, will be called the X1.
On the stage, a 20-piece swing band waited for its cue, while virtual curtains were pulled back on the cinema screen, and the first model was shown striding down the red carpet outside.
When the lights dimmed and the first model strutted out — strutted being the operative word — there was an audible gasp from the well-dressed crowd, which included Uma Thurman, Zachary Quinto and Emma Roberts.
The invention was unveiled to the public in April 1935 and the first model, the Model A, was made available in June of that year.
Although initially reported as the sixth design in an evolution of fighting knives and the first model in the lineup of Emerson's Specwar Custom Knives, Emerson later revealed that the knife was named for SEAL Team Six.
Similar(46)
And then the first model appears, very lightly made-up, her hair neatly parted and combed back into a low ponytail.
The analysis was carried out in three paired group models: AD HY and controls in the first model, AD + HY and controls in the second model, and AD HY and AD + HY in the third model.
The measure would not take effect until 2005, and the first models that would come under its restrictions would be sold in 2009.
The runway was a white glassy streak and the first models — Lindsey, Nyasha, Abbey Lee — came out with bouncy curls and pure white outfits tipped in pale sea prints.
When the hot Latino music came on and the first models stepped out in skintight sheaths ventilated under the bosom, it was as if Narcisco Rodriguez had opened a steam valve in the middle of the spring 2003 collections.
More suggestions(16)
and the first example
and the first pattern
and the first sample
and the first prototype
and the prior model
and the first modelling
and the initial model
and the highest model
and the first models
and the first modes
and the strongest model
and the first examples
and the first specimen
and the first mock up
and the biggest model
and the first formula
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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