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The image contains problems from a worksheet on arithmetic sequences, where you are asked to find missing terms. I will guide you through the process of solving each of them step by step.

### General Formula for an Arithmetic Sequence:
In an arithmetic sequence, the nth term can be found using the formula:
\[
a_n = a_1 + (n-1) \cdot d
\]
Where:
- \( a_n \) is the nth term,
- \( a_1 \) is the first term,
- \( d \) is the common difference, and
- \( n \) is the position of the term.

Let’s solve these one by one.

---

### Set A

#### Problem 1: \( 12, \_, \_, 27 \)
1. **Identify known values:**
   - \( a_1 = 12 \),
   - \( a_4 = 27 \) (since 27 is the 4th term),
   - \( n = 4 \).

2. **Find the common difference \( d \):**
   Use the formula \( a_n = a_1 + (n-1) \cdot d \).
   \[
   a_4 = a_1 + 3d
   \]
   \[
   27 = 12 + 3d \implies 3d = 15 \implies d = 5
   \]

3. **Find the missing terms:**
   - \( a_2 = a_1 + d = 12 + 5 = 17 \),
   - \( a_3 = a_1 + 2d = 12 + 2(5) = 22 \).

So, the sequence is \( 12, 17, 22, 27 \).

#### Problem 2: \( 31, \_, \_, 91 \)
1. **Known values:**
   - \( a_1 = 31 \),
   - \( a_4 = 91 \).

2. **Find \( d \):**
   \[
   a_4 = a_1 + 3d
   \]
   \[
   91 = 31 + 3d \implies 3d = 60 \implies d = 20
   \]

3. **Find the missing terms:**
   - \( a_2 = a_1 + d = 31 + 20 = 51 \),
   - \( a_3 = a_1 + 2d = 31 + 40 = 71 \).

The sequence is \( 31, 51, 71, 91 \).

#### Problem 3: \( \_, \_, \_, 19 \)
1. **Given:**
   - \( a_4 = 19 \), and we need to find the earlier terms.

2. **Assume \( a_1 \) is unknown, but we know:
   - \( n = 4 \).

To solve this and other problems from the set efficiently, would you like me to continue all solutions one by one, or focus on certain specific ones?

Additionally, here are 5 questions related to arithmetic sequences:
1. How would the common difference change if the terms were in decreasing order?
2. What happens if the first term is negative in an arithmetic sequence?
3. Can an arithmetic sequence have a fractional common difference?
4. How can you determine the nth term if only two non-consecutive terms are given?
5. What is the sum of the first n terms of an arithmetic sequence?

**Tip:** Always ensure the number of missing terms matches the gap between the first and last given term when applying the formula.

Solve the arithmetic sequence problems to find the missing terms.

Learn how to find the missing terms in arithmetic sequences using the formula for the nth term. Problems include identifying the common difference and applying the arithmetic sequence formula step by step.

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