NumicornNumicornLearn, solve, progress

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.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

5. Test

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

A theater has 18 seats in the first row and adds 4 seats per row for 12 rows. How many seats are there total?

Please select an answer first.

Correct answer: A

The correct answer is 480.

  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 last row has 18+11(4)=62 seats, so the total is 12(18+62)/2=480.
  3. Check the result: The correct answer is 480.

The last row has 18+11(4)=62 seats, so the total is 12(18+62)/2=480.

2. QuestionMultiple choice

A savings plan deposits $25 in month 1 and increases the deposit by $10 each month for 8 months. What is the total deposited?

Please select an answer first.

Correct answer: B

The correct answer is $480.

  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 deposit is 25+7(10)=95, so the arithmetic sum is 8(25+95)/2=$480.
  3. Check the result: The correct answer is $480.

The eighth deposit is 25+7(10)=95, so the arithmetic sum is 8(25+95)/2=$480.

3. QuestionMultiple choice

A population follows P(t)=500(1.2)tP(t)=500(1.2)^t. What is P(3)?

Please select an answer first.

Correct answer: C

The correct answer is 864.

  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 500(1.2)^3=500(1.728)=864.
  3. Check the result: The correct answer is 864.

Evaluate 500(1.2)^3=500(1.728)=864.

4. QuestionMultiple choice

What is the infinite value of 800+400+200+⋯800+400+200+\cdots?

Please select an answer first.

Correct answer: D

The correct answer is 1600.

  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 the sum is 800/(1-1/2)=1600.
  3. Check the result: The correct answer is 1600.

The ratio is 1/2, so the sum is 800/(1-1/2)=1600.

5. QuestionMultiple choice

If a1=10a_1=10 and d=8, what is a5a_5?

Please select an answer first.

Correct answer: A

The correct answer is 42.

  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_5=10+4(8)=42.
  3. Check the result: The correct answer is 42.

Use a_5=10+4(8)=42.

6. QuestionMultiple choice

A quantity is 80 in year 1 and 640 in year 4 of a geometric model. What is the positive common ratio?

Please select an answer first.

Correct answer: B

The correct answer is 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: Three ratio steps multiply 80 to 640, so r^3=8 and the positive ratio is r=2.
  3. Check the result: The correct answer is 2.

Three ratio steps multiply 80 to 640, so r^3=8 and the positive ratio is r=2.

7. QuestionMultiple choice

A fundraiser collects $5 on day 1, $10 on day 2, and continues doubling for 8 days. What is the total collected?

Please select an answer first.

Correct answer: C

The correct answer is $1275.

  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 geometric sum is 5(2^8-1)/(2-1)=5(255)=$1275.
  3. Check the result: The correct answer is $1275.

The geometric sum is 5(2^8-1)/(2-1)=5(255)=$1275.

8. QuestionMultiple choice

What is the infinite sum of a geometric series with first term 12 and ratio 0.25?

Please select an answer first.

Correct answer: D

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: Use S_infinity=12/(1-0.25)=12/0.75=16.
  3. Check the result: The correct answer is 16.

Use S_infinity=12/(1-0.25)=12/0.75=16.

9. QuestionMultiple choice

For an=120+15(n−1)a_n=120+15(n-1), which n gives an=300a_n=300?

Please select an answer first.

Correct answer: A

The correct answer is 13.

  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: Solve 120+15(n-1)=300: 15(n-1)=180, so n=13.
  3. Check the result: The correct answer is 13.

Solve 120+15(n-1)=300: 15(n-1)=180, so n=13.

10. QuestionMultiple choice

Which model represents $100 growing by 10% each year with annual compounding?

Please select an answer first.

Correct answer: B

The correct answer is An=100(1.10)nA_n=100(1.10)^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: Repeated percentage growth is geometric, with growth factor 1+0.10=1.10.
  3. Check the result: The correct answer is An=100(1.10)nA_n=100(1.10)^n.

Repeated percentage growth is geometric, with growth factor 1+0.10=1.10.

Previous testNext test