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Grade 11 · Math · Algebra 2

11th grade Series and sigma notation, and the sum of an arithmetic series worksheet

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Series and sigma notation, and the sum of an arithmetic series

Grade 11 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. Milo works out 11 + 14 + 17 + … + 71 on a math club card. What is the sum?

  2. Pia works out Σ from k = 1 to 20 of (3k + 2) on the class board. What is the sum?

  3. Ari's school hall has 16 rows. Row 1 has 20 seats, and each row has 2 more than the row before. How many seats are in the hall?

  4. Bo stacks cans for a food drive in 10 rows. The top row has 3 cans, and each row below has 1 more. How many cans are in the stack?

  5. Esme's grandparents put $15 into a savings fund in week 1, then $5 more each week than the week before. How many dollars are in the fund after 12 weeks?

  6. An outdoor theater has 18 rows. Row 1 has 24 seats, and each row has 3 more than the row before. How many seats does Jun count in all?

  7. Kira writes 5 + 8 + 11 + … + 32 in sigma notation. Which one is right?

    • Σ from k = 1 to 9 of (3k + 2)
    • Σ from k = 1 to 10 of (5k + 3)
    • Σ from k = 1 to 10 of (3k + 2)
    • Σ from k = 5 to 32 of k
    • Σ from k = 1 to 32 of (3k + 2)

  8. Luz writes 4 + 9 + 14 + … + 74 in sigma notation. Which one is right?

    • Σ from k = 4 to 74 of k
    • Σ from k = 1 to 14 of (5k − 1)
    • Σ from k = 1 to 15 of (5k − 1)
    • Σ from k = 1 to 74 of (5k − 1)
    • Σ from k = 1 to 15 of (4k + 5)

  9. Milo writes 9 + 11 + 13 + … + 47 in sigma notation. Which one is right?

    • Σ from k = 9 to 47 of k
    • Σ from k = 1 to 47 of (2k + 7)
    • Σ from k = 1 to 20 of (9k + 2)
    • Σ from k = 1 to 19 of (2k + 7)
    • Σ from k = 1 to 20 of (2k + 7)

  10. Noah writes 1 + 7 + 13 + … + 67 in sigma notation. Which one is right?

    • Σ from k = 1 to 67 of (6k − 5)
    • Σ from k = 1 to 12 of (6k − 5)
    • Σ from k = 1 to 67 of k
    • Σ from k = 1 to 11 of (6k − 5)
    • Σ from k = 1 to 12 of (k + 6)
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11th grade Series and sigma notation, and the sum of an arithmetic series worksheet – printable
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About this worksheet

Series and sigma notation, and the sum of an arithmetic series. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can keep a running total beside a growth table and read a partial sum from it.
  • I can add an arithmetic series by pairing the first and last terms: n(a₁ + aₙ)/2.
  • I can read and write sigma notation, count its terms, and find the sum of rows that do not start at 1.

Standard: A-SSE.B.4 (geometric series only; no CCSS code for arithmetic series)

Words to know

sequence: A list of numbers made by a rule: the term column of the table.

series: The terms of a sequence added up: the running-total column.

partial sum: The running total after some of the rows, like the total after row 6.

arithmetic series: A series whose terms grow by adding the same number each row.

sigma notation (Σ): A short way to write a sum: Σ from k = 1 to 5 of (2k + 3).

index (k): The row number in a sigma sum; it is put into the rule.

number of terms (n): How many rows are added: the arrows plus one.

Common mistakes

Gave the last term instead of the total of all the terms.

Stopped the running total one row early. Count the rows together, pointing at each one.

Multiplied the number of terms by the first plus the last term but did not halve. Add 1 + 2 + 3 + 4 by hand and compare with 4 × 5.

What to say

Ask: does the question want one row, or every row added?

Questions parents ask

What is the most common mistake with series and sigma notation, and the sum of an arithmetic series?

Gave the last term instead of the total of all the terms.

How can I help my child with series and sigma notation, and the sum of an arithmetic series?

Ask: does the question want one row, or every row added?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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