The image contains a math problem asking to find the "nth" term of each arithmetic sequence. There are five sequences provided, and the specific terms to be found are:

1. Sequence: 2, 5, 8, ... (Find the 97th term)
2. Sequence: 3, 5, 7, ... (Find the 200th term)
3. Sequence: 1, 12, 0, ... (Find the 16th term)
4. Sequence: 5, 11, 17, ... (Find the 99th term)
5. Sequence: 26, 22, 18, ... (Find the 40th term)

Solution Approach:

The general formula for the nth term of an arithmetic sequence is: $a_n = a_1 + (n-1) \times d$ Where:

• $a_n$ is the nth term,
• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Let's solve each sequence:

1. Sequence: 2, 5, 8, ...

• First term ($a_1$): 2
• Common difference ($d$): $5 - 2 = 3$
• Term to find: 97th term

$a_{97} = 2 + (97-1) \times 3 = 2 + 96 \times 3 = 2 + 288 = 290$

2. Sequence: 3, 5, 7, ...

• First term ($a_1$): 3
• Common difference ($d$): $5 - 3 = 2$
• Term to find: 200th term

$a_{200} = 3 + (200-1) \times 2 = 3 + 199 \times 2 = 3 + 398 = 401$

3. Sequence: 1, 12, 0, ...

• First term ($a_1$): 1
• Common difference ($d$): $12 - 1 = 11$
• Term to find: 16th term

$a_{16} = 1 + (16-1) \times 11 = 1 + 15 \times 11 = 1 + 165 = 166$

4. Sequence: 5, 11, 17, ...

• First term ($a_1$): 5
• Common difference ($d$): $11 - 5 = 6$
• Term to find: 99th term

$a_{99} = 5 + (99-1) \times 6 = 5 + 98 \times 6 = 5 + 588 = 593$

5. Sequence: 26, 22, 18, ...

• First term ($a_1$): 26
• Common difference ($d$): $22 - 26 = -4$
• Term to find: 40th term

$a_{40} = 26 + (40-1) \times (-4) = 26 + 39 \times (-4) = 26 - 156 = -130$

Final Answers:

1. 97th term: 290
2. 200th term: 401
3. 16th term: 166
4. 99th term: 593
5. 40th term: -130

Would you like further details or have any questions about this solution?

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Related Questions:

1. How do you find the common difference in an arithmetic sequence?
2. What is the sum of the first n terms of an arithmetic sequence?
3. How do you derive the formula for the nth term of an arithmetic sequence?
4. Can arithmetic sequences have a negative common difference?
5. What happens if the common difference in an arithmetic sequence is zero?
6. How does an arithmetic sequence differ from a geometric sequence?
7. Can the terms of an arithmetic sequence be fractions or decimals?
8. How would you solve for the 0th term in an arithmetic sequence?

Tip:

When solving arithmetic sequences, always double-check your common difference $d$ to ensure accuracy throughout your calculations.