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 - Building Confidence

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Read this first
Growth table (row | cans | running total)
1 | 2 | 2; 2 | 3 | 5; 3 | 4 | 9; the rows go on, + 1 on each arrow.
Bo stacks cans in rows, and each row down has 1 more can than the row above. How many cans are in the top 7 rows together?
Growth table (step | blocks | running total)
1 | 3 | 3; 2 | 6 | 9; 3 | 9 | 18; the rows go on, + 3 on each arrow.
Jun builds a staircase model, and each step uses 3 more blocks than the step before. How many blocks do steps 1 to 5 use in all?
Kira pairs the 10 terms of 3 + 7 + 11 + … + 39 from both ends, and each pair adds to 42. What is the sum?
Noah pairs the 11 terms of 2 + 5 + 8 + … + 32 from both ends, and each pair adds to 34. What is the sum?
Ren expands Σ from k = 1 to 6 of (3k − 1) on the class board. The expanded row starts with 2 and 5. What is the sum?
Tala expands Σ from k = 0 to 5 of (4k + 1) on the class board. The expanded row starts with 1 and 5. What is the sum?
Ari counts the terms of Σ from k = 4 to 15 of (2k − 1). How many terms are there?
Bo counts the terms of Σ from k = 3 to 20 of (3k + 1). How many terms are there?
Esme counts the terms of 7 + 11 + 15 + … + 83. How many terms are there?
Jun counts the terms of 5 + 8 + 11 + … + 65. How many terms are there?

11th grade Series and sigma notation, and the sum of an arithmetic series worksheet – printable — Print: 1 2 3 4 5 6

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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