Series · Grades 11–11

Series Worksheets

Summing arithmetic and geometric sequences with the standard closed-form formulas, every answer is an exact whole number, verified by the same math that produced the question.

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What it is

A series is the SUM of a sequence's terms, not the terms themselves, sequences list values, series add them up. An arithmetic series sums a sequence that adds the same amount each time; a geometric series sums one that multiplies by the same amount each time.

Why it matters

Series build directly on sequences and are a core pre-calculus topic, connecting to compound interest, population growth, and eventually calculus' infinite series. Recognizing when to add versus multiply terms is the key conceptual leap from sequences to series.

How to do it

  1. Identify whether the sequence is arithmetic (constant difference) or geometric (constant ratio).
  2. Arithmetic: S = n(a₁ + aₙ) ÷ 2, n is the number of terms, a₁ the first term, aₙ the last term summed.
  3. Geometric: S = a₁(rⁿ − 1) ÷ (r − 1), r is the common ratio.

Examples by level

  • BeginnerFind the sum of the first 4 terms: 1, 6, 11, … (arithmetic, d = 5) =34
  • IntermediateFind the sum of the first 4 terms: 8, 16, 32, … (geometric, r = 2) =120
  • AdvancedFind the sum of the first 4 terms: 10, 16, 22, … (arithmetic, d = 6) =76

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

  • Confusing the sum (series) with the last term (sequence), the question asks for one specific thing, not the other.
  • Using the wrong formula for arithmetic vs geometric.
  • Miscounting the number of terms n, especially when only the first few terms are shown.

Tips

  • Don't confuse the LAST term (aₙ) with the SUM, the sum is always bigger, since it's every term added together.
  • For a geometric series, the sum grows very fast, double-check whether the question wants the nth term or the total sum.

For parents

Connect this to something concrete: saving $10 more each week (arithmetic) versus doubling your savings each week (geometric), and ask which one grows faster.

For teachers

This directly extends the sequences skill, assigning both together makes the sequence-vs-series distinction (list the terms vs. add them up) concrete.

Key vocabulary

series
the sum of the terms of a sequence
common ratio
the fixed number each term in a geometric sequence is multiplied by to get the next term

Frequently asked questions

What grade is series taught in?
Grade 11, alongside sequences, as part of a functions course (Ontario's Discrete Functions strand).
What's the difference between a sequence and a series?
A sequence is an ordered list of terms. A series is the sum of those terms, sequences list, series add.

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