Correct answer: A

The correct answer is $a_n=3n+2$.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: The common difference is 3, so a_n = 5 + (n-1)3 = 3n+2.
3. Check the result: The correct answer is $a_n=3n+2$.

Correct answer: B

The correct answer is -5.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: Subtract consecutive terms: 7 - 12 = -5, and the same difference continues.
3. Check the result: The correct answer is -5.

Correct answer: C

The correct answer is 58.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: Use a_n=a_1+(n-1)d: a_10=4+9(6)=58.
3. Check the result: The correct answer is 58.

Correct answer: D

The correct answer is 9.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: Substitute n=5: a_5=2(5)-1=9.
3. Check the result: The correct answer is 9.

Correct answer: A

The correct answer is 0.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: The common difference is -5, so the next term is 5-5=0.
3. Check the result: The correct answer is 0.

Correct answer: B

The correct answer is 16.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: Starting with 7, add 3 three times: a_2=10, a_3=13, a_4=16.
3. Check the result: The correct answer is 16.

Correct answer: C

The correct answer is 40.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: The fifth term is 14, so S_5=5(2+14)/2=40.
3. Check the result: The correct answer is 40.

Correct answer: D

The correct answer is $S_n=\frac{n}{2}(a_1+a_n)$.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: An arithmetic-series sum is the number of terms times the average of the first and last terms.
3. Check the result: The correct answer is $S_n=\frac{n}{2}(a_1+a_n)$.

Correct answer: A

The correct answer is 3.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: Five steps increase the sequence by 25-10=15, so d=15/5=3.
3. Check the result: The correct answer is 3.

Correct answer: B

The correct answer is $a_n=3n-7$.

1. Identify the sequence or series structure: Determine whether the terms have a common difference, common ratio, recursive rule, explicit rule, or summation pattern.
2. Apply the sequence or series relationship: The difference is 3 and a_1=-4, so a_n=-4+(n-1)3=3n-7.
3. Check the result: The correct answer is $a_n=3n-7$.