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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 ∑k=110k\sum_{k=1}^{10}k?

Please select an answer first.

Correct answer: A

The correct answer is 55.

  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 sum of the first 10 positive integers is 10(11)/2=55.
  3. Check the result: The correct answer is 55.

The sum of the first 10 positive integers is 10(11)/2=55.

2. QuestionMultiple choice

What is the sum of the first 8 terms of 7, 10, 13, ...?

Please select an answer first.

Correct answer: B

The correct answer is 140.

  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 eighth term is 28, so S_8=8(7+28)/2=140.
  3. Check the result: The correct answer is 140.

The eighth term is 28, so S_8=8(7+28)/2=140.

3. QuestionMultiple choice

What is 2+4+8+16+322+4+8+16+32?

Please select an answer first.

Correct answer: C

The correct answer is 62.

  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 five geometric terms: 2+4+8+16+32=62.
  3. Check the result: The correct answer is 62.

Add the five geometric terms: 2+4+8+16+32=62.

4. QuestionMultiple choice

What is the infinite sum 6+3+1.5+⋯6+3+1.5+\cdots?

Please select an answer first.

Correct answer: D

The correct answer is 12.

  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 S_infinity=a_1/(1-r)=6/(1-1/2)=12.
  3. Check the result: The correct answer is 12.

Use S_infinity=a_1/(1-r)=6/(1-1/2)=12.

5. QuestionMultiple choice

When does an infinite geometric series converge?

Please select an answer first.

Correct answer: A

The correct answer is ∣r∣<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 terms approach zero and the infinite sum exists only when the absolute value of r is less than 1.
  3. Check the result: The correct answer is ∣r∣<1|r|<1.

The terms approach zero and the infinite sum exists only when the absolute value of r is less than 1.

6. QuestionMultiple choice

What is ∑k=14k2\sum_{k=1}^{4}k^2?

Please select an answer first.

Correct answer: B

The correct answer is 30.

  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 1^2+2^2+3^2+4^2=1+4+9+16=30.
  3. Check the result: The correct answer is 30.

Evaluate 1^2+2^2+3^2+4^2=1+4+9+16=30.

7. QuestionMultiple choice

If a1=6a_1=6 and d=4, what is a6a_6?

Please select an answer first.

Correct answer: C

The correct answer is 26.

  1. Identify the sequence or series structure: This is an arithmetic sequence with first term 6, common difference 4, and index 6.
  2. Apply the sequence or series relationship: Use a_n=a_1+(n-1)d: a_6=6+5(4)=26.
  3. Check the result: The sixth term is 26.

Use a_n=a_1+(n-1)d: a_6=6+5(4)=26.

8. QuestionMultiple choice

What is 3−6+12−24+483-6+12-24+48?

Please select an answer first.

Correct answer: D

The correct answer is 33.

  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: This is a five-term geometric sum with a_1=3 and r=-2: 3-6+12-24+48=33.
  3. Check the result: The correct answer is 33.

This is a five-term geometric sum with a_1=3 and r=-2: 3-6+12-24+48=33.

9. QuestionMultiple choice

What is the infinite sum 10+5+2.5+⋯10+5+2.5+\cdots?

Please select an answer first.

Correct answer: A

The correct answer is 20.

  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 ratio is 1/2, so S_infinity=10/(1-1/2)=20.
  3. Check the result: The correct answer is 20.

The ratio is 1/2, so S_infinity=10/(1-1/2)=20.

10. QuestionMultiple choice

What is 1+13+19+⋯1+\frac13+\frac19+\cdots?

Please select an answer first.

Correct answer: B

The correct answer is 32\frac32.

  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: This infinite geometric series has sum 1/(1-1/3)=3/2.
  3. Check the result: The correct answer is 32\frac32.

This infinite geometric series has sum 1/(1-1/3)=3/2.

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