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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 the common ratio of 2, 6, 18, 54, ...?

Please select an answer first.

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: Divide consecutive terms: 6/2=3, and the same ratio continues.
  3. Check the result: The correct answer is 3.

Divide consecutive terms: 6/2=3, and the same ratio continues.

2. QuestionMultiple choice

If a1=5a_1=5 and r=2r=2, what is a6a_6?

Please select an answer first.

Correct answer: B

The correct answer is 160.

  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_1r^(n-1): a_6=5(2^5)=160.
  3. Check the result: The correct answer is 160.

Use a_n=a_1r^(n-1): a_6=5(2^5)=160.

3. QuestionMultiple choice

If an=3⋅2n−1a_n=3\cdot2^{n-1}, what is a4a_4?

Please select an answer first.

Correct answer: C

The correct answer is 24.

  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=4: a_4=3(2^3)=24.
  3. Check the result: The correct answer is 24.

Substitute n=4: a_4=3(2^3)=24.

4. QuestionMultiple choice

What is the next term in 81, 27, 9, ...?

Please select an answer first.

Correct answer: D

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: Each term is divided by 3, so 9/3=3.
  3. Check the result: The correct answer is 3.

Each term is divided by 3, so 9/3=3.

5. QuestionMultiple choice

A sequence is defined by a1=4a_1=4 and an=2an−1a_n=2a_{n-1}. What is a3a_3?

Please select an answer first.

Correct answer: A

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: Double twice: a_2=8 and a_3=16.
  3. Check the result: The correct answer is 16.

Double twice: a_2=8 and a_3=16.

6. QuestionMultiple choice

What is the sum of the first 4 terms of 3, 6, 12, 24, ...?

Please select an answer first.

Correct answer: B

The correct answer is 45.

  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: Add the first four terms: 3+6+12+24=45.
  3. Check the result: The correct answer is 45.

Add the first four terms: 3+6+12+24=45.

7. QuestionMultiple choice

Which formula gives the sum of the first n terms of a geometric sequence when r≠1r\ne1?

Please select an answer first.

Correct answer: C

The correct answer is Sn=a1rn−1r−1S_n=a_1\frac{r^n-1}{r-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: The finite geometric-series formula is a_1(r^n-1)/(r-1).
  3. Check the result: The correct answer is Sn=a1rn−1r−1S_n=a_1\frac{r^n-1}{r-1}.

The finite geometric-series formula is a_1(r^n-1)/(r-1).

8. QuestionMultiple choice

If a2=12a_2=12 and a3=36a_3=36 in a geometric sequence, what is r?

Please select an answer first.

Correct answer: D

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: The common ratio is a_3/a_2=36/12=3.
  3. Check the result: The correct answer is 3.

The common ratio is a_3/a_2=36/12=3.

9. QuestionMultiple choice

What is the next term in 5, -10, 20, -40, ...?

Please select an answer first.

Correct answer: A

The correct answer is 80.

  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 ratio is -2, so -40(-2)=80.
  3. Check the result: The correct answer is 80.

The common ratio is -2, so -40(-2)=80.

10. QuestionMultiple choice

What is true of a geometric sequence with common ratio 1?

Please select an answer first.

Correct answer: B

The correct answer is All terms are equal..

  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: Multiplying by 1 leaves every term equal to the first term.
  3. Check the result: The correct answer is All terms are equal..

Multiplying by 1 leaves every term equal to the first term.

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