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Sequences and Series Practice Tests

These Grade 11 Math practice tests develop sequence and series skills across arithmetic and geometric patterns, explicit and recursive formulas, finite sums, infinite geometric series, sigma notation, and applications.

Skills covered

  • Finding common differences, common ratios, nth terms, and recursive rules
  • Using arithmetic and geometric sequence formulas
  • Calculating finite arithmetic and geometric sums
  • Evaluating sigma notation and determining when infinite geometric series converge
  • Applying sequence and series models to savings, population, seating, growth, decay, and other contexts

How to use these practice tests

Check whether the pattern is additive or multiplicative before selecting a formula. Track the indexing carefully, identify the first term and number of terms, and verify whether an infinite sum is convergent.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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Grade 11 Sequences and Series Practice Tests

Practice Grade 11 Math questions about arithmetic and geometric sequences, explicit and recursive rules, finite and infinite series, sigma notation, and applications.

Choose the best answer. Identify the common difference or ratio, select the correct sequence or series formula, and interpret the result in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is an explicit formula for 6, 10, 14, 18, ...?

Please select an answer first.

Correct answer: A

The correct answer is an=4n+2a_n=4n+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 difference is 4 and a_1=6, so a_n=6+(n-1)4=4n+2.
  3. Check the result: The correct answer is an=4n+2a_n=4n+2.

The difference is 4 and a_1=6, so a_n=6+(n-1)4=4n+2.

2. QuestionMultiple choice

Which recursive rule generates 3, -6, 12, -24, ...?

Please select an answer first.

Correct answer: B

The correct answer is a1=3, an=−2an−1a_1=3,\ a_n=-2a_{n-1}.

  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: Each term is multiplied by -2, beginning with a_1=3.
  3. Check the result: The correct answer is a1=3, an=−2an−1a_1=3,\ a_n=-2a_{n-1}.

Each term is multiplied by -2, beginning with a_1=3.

3. QuestionMultiple choice

What is the common difference of 4, 9, 14, 19, ...?

Please select an answer first.

Correct answer: C

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: 9-4=5.
  3. Check the result: The correct answer is 5.

Subtract consecutive terms: 9-4=5.

4. QuestionMultiple choice

What type of sequence is 2, 4, 8, 16, ...?

Please select an answer first.

Correct answer: D

The correct answer is Geometric.

  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: Each term is multiplied by the constant ratio 2.
  3. Check the result: The correct answer is Geometric.

Each term is multiplied by the constant ratio 2.

5. QuestionMultiple choice

If a1=7a_1=7 and d=-2, which is the explicit formula?

Please select an answer first.

Correct answer: A

The correct answer is an=9−2na_n=9-2n.

  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=7+(n-1)(-2)=9-2n.
  3. Check the result: The correct answer is an=9−2na_n=9-2n.

Use a_n=7+(n-1)(-2)=9-2n.

6. QuestionMultiple choice

A student saves $20 in week 1 and adds $5 each week. How much is saved in week 10?

Please select an answer first.

Correct answer: B

The correct answer is $65.

  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 arithmetic sequence gives a_10=20+9(5)=65.
  3. Check the result: The correct answer is $65.

The arithmetic sequence gives a_10=20+9(5)=65.

7. QuestionMultiple choice

A culture starts with 3 bacteria and doubles each day. How many are present on day 5?

Please select an answer first.

Correct answer: C

The correct answer is 48.

  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: Day 5 is 3(2^4)=48 because day 1 is the initial term.
  3. Check the result: The correct answer is 48.

Day 5 is 3(2^4)=48 because day 1 is the initial term.

8. QuestionMultiple choice

A value follows V(t)=1000(0.8)tV(t)=1000(0.8)^t. What is V(3)?

Please select an answer first.

Correct answer: D

The correct answer is 512.

  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: Evaluate 1000(0.8)^3=1000(0.512)=512.
  3. Check the result: The correct answer is 512.

Evaluate 1000(0.8)^3=1000(0.512)=512.

9. QuestionMultiple choice

Which explicit formula matches a1=5a_1=5 and an=3an−1a_n=3a_{n-1}?

Please select an answer first.

Correct answer: A

The correct answer is an=5⋅3n−1a_n=5\cdot3^{n-1}.

  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: A geometric sequence has a_n=a_1r^(n-1)=5·3^(n-1).
  3. Check the result: The correct answer is an=5⋅3n−1a_n=5\cdot3^{n-1}.

A geometric sequence has a_n=a_1r^(n-1)=5·3^(n-1).

10. QuestionMultiple choice

What type of pattern is suggested by constant second differences?

Please select an answer first.

Correct answer: B

The correct answer is A quadratic sequence.

  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: Constant second differences indicate that the first differences change linearly, which is characteristic of a quadratic rule.
  3. Check the result: The correct answer is A quadratic sequence.

Constant second differences indicate that the first differences change linearly, which is characteristic of a quadratic rule.

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