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 - Challenge Me

NameDate

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

After row 11, 154; after row 12, 186; after row 30, 1275. Pia wants the sum of rows 12 to 30 of a(k) = 3k − 4, using the running totals shown. What is that sum?
After row 7, 105; after row 8, 128; after row 25, 825. Ren wants the sum of rows 8 to 25 of a(k) = 2k + 7, using the running totals shown. What is that sum?
After row 9, 243; after row 10, 295; after row 24, 1548. Tala wants the sum of rows 10 to 24 of a(k) = 5k + 2, using the running totals shown. What is that sum?
Zee works out Σ from k = 6 to 30 of (45 − 2k) for math club. What is the sum?
Ari works out Σ from k = 3 to 24 of (60 − 4k) for math club. What is the sum?
A hall's first row has 18 seats, each row has 2 more than the row before, and the last row has 52. How many seats does Esme count in all?
Jun builds a can display. The top row has 3 cans, each row below has 1 more, and the bottom row has 15. How many cans are in the display?
Milo's school hall has 15 rows and 525 seats. Row 1 has 21 seats, and each row has the same number more than the row before. How many seats are in the last row?
A can display has 11 rows and 99 cans. The top row has 4 cans, and each row below has the same number more. How many cans does Noah put in the bottom row?
Pia's grandparents put $900 into a savings fund over 12 weeks, adding the same amount more each week. Week 1 was $20. How many dollars went in during week 12?

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.

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)

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.

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.

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

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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