Arithmetic sequence problems worksheet for finding specific terms.

To solve the problems, we need to identify the pattern in each sequence and then use that pattern to find the specified term. Let's go through each sequence step by step.

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Sequence 1: \( 16, 20, 24, 28, 32, \ldots \)

#### Step 1: Identify the pattern
The sequence increases by a constant difference:
\[
20 - 16 = 4, \quad 24 - 20 = 4, \quad 28 - 24 = 4, \quad 32 - 28 = 4
\]
So, the common difference is \( d = 4 \).

#### Step 2: General formula for an arithmetic sequence
The \( n \)-th term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n-1)d
\]
where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

Here, \( a_1 = 16 \) and \( d = 4 \).

#### Step 3: Find the 22nd term
\[
a_{22} = 16 + (22-1) \cdot 4
\]
\[
a_{22} = 16 + 21 \cdot 4
\]
\[
a_{22} = 16 + 84
\]
\[
a_{22} = 100
\]

#### Answer:
\[
\boxed{100}
\]

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Sequence 2: \( 3, 9, 15, 21, 27, \ldots \)

#### Step 1: Identify the pattern
The sequence increases by a constant difference:
\[
9 - 3 = 6, \quad 15 - 9 = 6, \quad 21 - 15 = 6, \quad 27 - 21 = 6
\]
So, the common difference is \( d = 6 \).

#### Step 2: General formula for an arithmetic sequence
Using the formula \( a_n = a_1 + (n-1)d \):
Here, \( a_1 = 3 \) and \( d = 6 \).

#### Step 3: Find the 21st term
\[
a_{21} = 3 + (21-1) \cdot 6
\]
\[
a_{21} = 3 + 20 \cdot 6
\]
\[
a_{21} = 3 + 120
\]
\[
a_{21} = 123
\]

#### Answer:
\[
\boxed{123}
\]

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Sequence 3: \( 2, 4, 6, 8, 10, \ldots \)

#### Step 1: Identify the pattern
The sequence increases by a constant difference:
\[
4 - 2 = 2, \quad 6 - 4 = 2, \quad 8 - 6 = 2, \quad 10 - 8 = 2
\]
So, the common difference is \( d = 2 \).

#### Step 2: General formula for an arithmetic sequence
Using the formula \( a_n = a_1 + (n-1)d \):
Here, \( a_1 = 2 \) and \( d = 2 \).

#### Step 3: Find the 18th term
\[
a_{18} = 2 + (18-1) \cdot 2
\]
\[
a_{18} = 2 + 17 \cdot 2
\]
\[
a_{18} = 2 + 34
\]
\[
a_{18} = 36
\]

#### Answer:
\[
\boxed{36}
\]

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Sequence 4: \( 10, 22, 34, 46, 58, \ldots \)

#### Step 1: Identify the pattern
The sequence increases by a constant difference:
\[
22 - 10 = 12, \quad 34 - 22 = 12, \quad 46 - 34 = 12, \quad 58 - 46 = 12
\]
So, the common difference is \( d = 12 \).

#### Step 2: General formula for an arithmetic sequence
Using the formula \( a_n = a_1 + (n-1)d \):
Here, \( a_1 = 10 \) and \( d = 12 \).

#### Step 3: Find the 19th term
\[
a_{19} = 10 + (19-1) \cdot 12
\]
\[
a_{19} = 10 + 18 \cdot 12
\]
\[
a_{19} = 10 + 216
\]
\[
a_{19} = 226
\]

#### Answer:
\[
\boxed{226}
\]

---

Sequence 5: \( 22, 27, 32, 37, 42, \ldots \)

#### Step 1: Identify the pattern
The sequence increases by a constant difference:
\[
27 - 22 = 5, \quad 32 - 27 = 5, \quad 37 - 32 = 5, \quad 42 - 37 = 5
\]
So, the common difference is \( d = 5 \).

#### Step 2: General formula for an arithmetic sequence
Using the formula \( a_n = a_1 + (n-1)d \):
Here, \( a_1 = 22 \) and \( d = 5 \).

#### Step 3: Find the 33rd term
\[
a_{33} = 22 + (33-1) \cdot 5
\]
\[
a_{33} = 22 + 32 \cdot 5
\]
\[
a_{33} = 22 + 160
\]
\[
a_{33} = 182
\]

#### Answer:
\[
\boxed{182}
\]

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Final Answers:

1. \( \boxed{100} \)
2. \( \boxed{123} \)
3. \( \boxed{36} \)
4. \( \boxed{226} \)
5. \( \boxed{182} \)