а₁ = 10, a, 19.

It appears you are listing terms in a sequence. The first term \( a₁ \) is given as 10, and the third term is given as 19. Since you only provided three elements and the second element (a) is not specified, I'll assume you are implying that the sequence may have a specific pattern and you might be looking for the term "a" or a general formula for the sequence.

To determine the nature of the sequence and find the second term "a", we first need to investigate the relation between the terms you've given. If we assume the sequence progresses in a linear fashion (each term increases or decreases by a constant difference), we can find the common difference.

If the sequence is an arithmetic sequence (each term is the previous term plus a constant difference, d), the second term would be:

\( a₂ = a₁ + d \)

and the third term would be:

\( a₃ = a₁ + 2d \)

Using the terms you've provided (10 and 19 for \( a₁ \) and \( a₃ \) respectively), we can solve for the common difference:

\( 19 = 10 + 2d \)

\( 2d = 19 - 10 \)

\( 2d = 9 \)

\( d = \frac{9}{2} \)

\( d = 4.5 \)

Now we can find the second term (a):

\( a = a₁ + d \)

\( a = 10 + 4.5 \)

\( a = 14.5 \)

So if the sequence is an arithmetic sequence, the second term would be 14.5.