Grade 11 Sequences & Series Worksheets
Free printable sequences & series practice for Grade 11 students. Generate problems, solve them on screen or paper, and download as PDF.
Practice Worksheet
Grade 11 Sequences & Series Practice
Solve each problem. Show your work.
- 1.An arithmetic sequence has a₁ = 6 and d = 2. Find a8: _____
- 2.A geometric sequence has a₁ = 5 and r = 2. Find a5: _____
- 3.Find the sum of the first 10 terms when a₁ = 2 and d = 3: _____
- 4.An arithmetic sequence has a₁ = 5 and d = 3. Find a8: _____
- 5.A geometric sequence has a₁ = 7 and r = 3. Find a5: _____
- 6.Find the sum of the first 10 terms when a₁ = 3 and d = 4: _____
Show answer key
- Question 1: 20
- Question 2: 80
- Question 3: 155
- Question 4: 26
- Question 5: 567
- Question 6: 210
Free Practice Worksheets
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Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Find the 10th term of the arithmetic sequence where the first term a = 3 and the common difference d = 5 using the explicit formula a_n = a + (n - 1)d.
- 2.Find the 6th term of the geometric sequence where the first term a = 2 and the common ratio r = 3 using the explicit formula a_n = a * r^(n - 1).
- 3.Write the first 4 terms of the sequence defined by the recursive formula: a_1 = 4 and a_n = a_(n-1) + 6.
- 4.Calculate the sum of the first 10 terms of the arithmetic series with a_1 = 2 and a_10 = 20 using the formula S_n = n/2 * (a_1 + a_n).
- 5.Calculate the sum of the first 5 terms of the geometric series with a = 3 and r = 2 using the formula S_n = a(1 - r^n) / (1 - r).
- 6.Calculate the future value (FV) of an annuity with regular payments R = 100, interest rate i = 0.05, and n = 3 periods using the formula FV = R * ((1 + i)^n - 1) / i.
A selection of topic skills
Solve each problem. Show your work.
- 1.Find the 15th term of an arithmetic sequence where the first term is 7 and the common difference is -3. Write the explicit formula for the sequence.
- 2.A geometric sequence has a second term of 6 and a fourth term of 54. Find the common ratio (r > 0) and the first term, then write the recursive formula.
- 3.Calculate the sum of the first 20 terms of the arithmetic series: 5 + 12 + 19 + 26 + ...
- 4.A ball is dropped from a height of 10 meters. Each time it hits the ground, it bounces to 80% of its previous height. Find the total vertical distance the ball has traveled when it hits the ground for the 5th time.
- 5.An investor deposits 500 into an account at the end of every month for 5 years. The account earns 6% annual interest, compounded monthly (0.5% per month). Using the future value of an ordinary annuity formula, how much money will be in the account after 5 years?
- 6.Compare the growth of two sequences. Sequence A is arithmetic with a1 = 10 and d = 5. Sequence B is geometric with b1 = 2 and r = 2. Which sequence has a larger 7th term?
What Your Child Will Learn
The discrete functions unit shifts from continuous graphs to sequences — ordered lists of numbers following a predictable pattern. Students distinguish arithmetic sequences (constant common difference) from geometric sequences (constant common ratio), and derive both recursive formulas (each term defined from the previous one) and explicit formulas (any term calculated directly from its position).
Series — the sums of sequence terms — follow naturally, with students applying and deriving the summation formulas for arithmetic and geometric series and using them to solve problems involving total accumulated quantities. A major applied strand is annuities and financial applications: students calculate the future value of regular deposits and the present value of a loan being paid off, connecting geometric series directly to real savings and borrowing scenarios.
This unit rewards careful pattern recognition and precise formula selection — mixing up an arithmetic and geometric formula, or a recursive and explicit one, is the most common source of errors. Because annuities appear on many standardized tests and personal finance contexts beyond school, this unit has practical value well past the course itself.
Skills Covered
- Identifying arithmetic and geometric sequences from a pattern
- Writing recursive and explicit (general term) formulas for sequences
- Calculating the sum of arithmetic and geometric series
- Solving problems involving future value of an annuity
- Solving problems involving present value of an annuity or loan
- Distinguishing which sequence or series formula applies to a given problem
Curriculum Aligned: Strand of Grade 11 Functions (MCR3U) covering sequences, series, and their financial applications through simple annuities.
Parent Tip: Since annuity and loan problems mirror real financial products, you can sanity-check an answer using a free online loan or savings calculator rather than redoing the series formula yourself — if the numbers are in the same ballpark, that's a reasonable confidence check.
What your child will practice
- AnnuitiesSolve problems involving present value and future value of annuities.
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Check my workFrequently Asked Questions
How often should my child practice sequences & series?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.