Series Identification: Arithmetic Progression

The given series is $8, 19, 30, \dots$. To understand the pattern, let's find the difference between consecutive terms:

• $19 - 8 = 11$
• $30 - 19 = 11$

Since the difference between consecutive terms is constant (11), this is an arithmetic progression (AP). In an AP, each term after the first is obtained by adding a fixed, non-zero number called the common difference.

Calculating the 10th Term

We need to find the 10th term of this series. We can use the formula for the $n$-th term of an arithmetic progression:

$$a_n = a_1 + (n-1)d$$

Where:

• $a_n$ is the $n$-th term (the term we want to find).
• $a_1$ is the first term of the series.
• $n$ is the term number.
• $d$ is the common difference.

Applying the Formula

From the given series $8, 19, 30, \dots$:

• The first term, $a_1 = 8$.
• The common difference, $d = 11$.
• We want to find the 10th term, so $n = 10$.

Step-by-Step Calculation

1. Substitute the values into the formula:

   $$a_{10} = 8 + (10-1) \times 11$$

2. Calculate the value inside the parenthesis:

   $$a_{10} = 8 + (9) \times 11$$

3. Perform the multiplication:

   $$a_{10} = 8 + 99$$

4. Perform the addition:

   $$a_{10} = 107$$

Therefore, the 10th term of the arithmetic series $8, 19, 30, \dots$ is 107.