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 = 6 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 = 3 and d = 3. Find a8: _____
- 5.A geometric sequence has a₁ = 4 and r = 3. Find a5: _____
- 6.Find the sum of the first 10 terms when a₁ = 5 and d = 4: _____
Show answer key
- Question 1: 20
- Question 2: 96
- Question 3: 155
- Question 4: 24
- Question 5: 324
- Question 6: 230
Free Practice Worksheets
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Build confidence with approachable problems
Solve each problem. Show your work clearly.
- 1.Find the 10th term of the arithmetic sequence where the first term (a) is 5 and the common difference (d) is 3. Use the explicit formula: an = a + (n - 1)d.
- 2.Find the 6th term of the geometric sequence where the first term (a) is 2 and the common ratio (r) is 3. Use the explicit formula: an = a * r^(n - 1).
- 3.Write the first 4 terms of the sequence defined by the recursive formula: a1 = 4 and an = an-1 + 5.
- 4.Calculate the sum of the first 10 terms of the arithmetic series where the first term is 2 and the 10th term is 20. Use the formula: Sn = n/2 * (a1 + an).
- 5.Calculate the sum of the first 5 terms of the geometric series where the first term is 3 and the common ratio is 2. Use the formula: Sn = a(1 - r^n) / (1 - r).
- 6.Calculate the future value (FV) of an annuity with a regular payment (PMT) of 100, an interest rate (i) of 0.05, and 4 periods (n). Use the formula: FV = PMT * [((1 + i)^n - 1) / i].
Full range of grade expectations
Solve each problem. Show your work.
- 1.Find the explicit formula for an arithmetic sequence where the 3rd term is 14 and the 8th term is 39. Then, determine the 20th term.
- 2.A geometric sequence is defined by the recursive formula a(n) = -2 * a(n-1) with a(1) = 3. Write the explicit formula and find the sum of the first 6 terms.
- 3.Compare the following two series: Series A is an arithmetic series with 10 terms where the first term is 5 and the last term is 50. Series B is a geometric series with 5 terms where the first term is 2 and the common ratio is 3. Which series has a greater sum?
- 4.Consider the sequence 1/2, 1/4, 1/8, 1/16... Determine if this sequence is arithmetic, geometric, or neither. If it is geometric, find the sum of the infinite series.
- 5.Word Problem: You deposit 200 dollars at the end of every month into a savings account that pays an annual interest rate of 6 percent, compounded monthly (0.5 percent per month). How much money will you have in the account after 3 years (36 months)? Use the formula for the future value of an ordinary annuity: FV = P * (((1 + r)^n - 1) / r).
- 6.Word Problem: A company's equipment depreciates in value every year. A machine purchased for 50,000 dollars loses 15 percent of its remaining value each year. Write a geometric sequence to represent the value of the machine at the end of each year and calculate its value after 5 years.
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.