А₁ = 10, a, 19.

It seems you've provided a sequence with the first and the third terms and want to find the second term, denoted as "a". Based on the provided terms, the sequence could potentially be an arithmetic sequence, although we can't be certain just with two terms. Let's try to see if it is an arithmetic sequence. An arithmetic sequence is characterized by a common difference between consecutive terms, and its general form is given by:

aₙ = a₁ + (n - 1)d

Where:

• aₙ is the nth term in the sequence
• a₁ is the first term in the sequence
• d is the common difference
• n is the term number

To determine if your sequence is arithmetic, let's assume that a₂ (the second term, which you've denoted as "a") indeed creates an arithmetic sequence with the first (a₁ = 10) and third (a₃ = 19) terms.

Using the formula for the nth term, the second term in the sequence would be represented as:

a₂ = a₁ + d

Since we are also given the third term, the formula would look like this:

a₃ = a₁ + 2d = 19

We know a₁ = 10, hence:

10 + 2d = 19

Now, let's solve for d:

2d = 19 - 10 2d = 9 d = 9 / 2 d = 4.5

Now that we have the common difference, we can find the second term:

a₂ = a₁ + d a₂ = 10 + 4.5 a₂ = 14.5

So the second term, "a," in your sequence is 14.5 if it is indeed an arithmetic sequence. The sequence is 10, 14.5, 19.

If the sequence is not arithmetic, or if you have additional information or constraints that apply, please provide them to help give you the correct answer.