Grade 11 Sequences & Series - Medium
A medium grade 11 worksheet for Sequences & Series.
Worksheet snapshot
- Sequences & Series
- Key concepts: Understanding core sequences & series concepts for Grade 11; Applying sequences & series strategies appropriate to Grade 11
- Students develop fluency with sequences & series at Grade 11 level, applying strategies more independently and solving increasingly complex problems.
- Apply it: Sequences & Series at the Grade 11 level connects to everyday situations students encounter: problem-solving in daily life, making sense of quantities and relationships, and building mathematical literacy for future learning.
- For the geometric sequence with a₁ = 4 and r = 2, find a_14.
- For the geometric sequence with a₁ = 2 and r = 3, find a_9.
- For the arithmetic sequence with a₁ = 10 and d = 4, find a_5.
About Sequences & Series
Sequences are ordered lists of numbers following a pattern. Series are sums of sequence terms. Students study arithmetic and geometric sequences and series, including formulas and applications.
Sequences and series model discrete growth, financial calculations (annuities), and patterns. They're fundamental to calculus (limits, infinite series) and many mathematical applications.
Sequences & Series
Analyze and generate arithmetic and geometric sequences; write recursive/explicit formulas; compute partial sums.
This medium level worksheet:
Write explicit formulas; find nth term; compute partial sums for arithmetic/geometric series.
Key Concepts
- Arithmetic vs. geometric patterns
- Recursive and explicit forms
- Partial sums and sigma notation
Prerequisite skills
Function representations; exponential/linear basics; algebraic manipulation.
Teaching Strategies
Use tables to detect difference/ratio; connect arithmetic↔linear and geometric↔exponential; derive sum formulas; use sigma notation stepwise.
Assessment ideas
Test sequence pattern recognition and formula use. Include series sum calculations. Ask students to write recursive and explicit formulas. Use real applications (loan payments, population models).
Common Challenges
Mixing up difference vs. ratio; indexing mistakes; misusing sum formulas.
Real-World Applications
Savings plans, depreciation, population growth, tiling/pattern counts.
Extension Activities
Compare recursive vs. explicit efficiency; derive geometric sum in a context; interpret sigma notation in word form.
Parent Tips
Ask your student to classify a sequence quickly (arithmetic or geometric) and justify with difference/ratio.