PencilGo

Grade 11 · Math · Algebra 2

11th grade Sum of a finite geometric series, and infinite geometric series worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version
Print

Sum of a finite geometric series, and infinite geometric series

Grade 11 Math Worksheet

NameDate

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

  1. Ari works out 3 + 6 + 12 + … + 384 on a math club card. What is the sum?

  2. Bo works out 5 + 15 + 45 + … + 1215 on a math club card. What is the sum?

  3. Luz writes the infinite series 48 + 12 + 3 + … on the class board. What number does its running total approach?

  4. Milo writes the infinite series 20 − 10 + 5 − … on the class board. What number does its running total approach?

  5. Ren's parents add $500 to a savings fund at the end of each year, and it grows 3% a year. To the nearest cent, what does it hold right after deposit 6?

  6. Tala's grandparents add $100 to a savings fund at the end of each year, and it grows 5% a year. To the nearest cent, what does it hold right after deposit 10?

  7. Zee's parents add $250 to a savings fund at the end of each year, and it grows 2% a year. To the nearest cent, what does it hold right after deposit 8?

  8. Bo writes the infinite series 27 − 9 + 3 − … on the class board. Which statement about its total is right?

    • Total 20.25, since 27 ÷ (1 − (-1/3)) = 20.25
    • No total, since the terms never reach 0 and keep going
    • Total -81, since 27 ÷ (-1/3) = -81
    • Total 21, the sum of the terms shown

  9. Esme writes the infinite series 16 + 20 + 25 + … on the class board. Which statement about its total is right?

    • No total, since r = 5/4 and the terms keep growing
    • Total 12.8, since 16 ÷ (5/4) = 12.8
    • Total -64, since 16 ÷ (1 − 5/4) = -64, applying the formula anyway
    • Total 61, the sum of the terms shown

  10. Jun writes the infinite series 8 − 12 + 18 − … on the class board. Which statement about its total is right?

    • Total 3.2, since 8 ÷ (1 − (-3/2)) = 3.2
    • Total -16/3, since 8 ÷ (-3/2) = -16/3
    • No total, since r = -3/2 and the total swings further each time
    • Total 14, the sum of the terms shown
PencilGopencilgo.com

11th grade Sum of a finite geometric series, and infinite geometric series worksheet – printable
Print: 123456

About this worksheet

Sums of finite and infinite geometric 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 of a geometric table and use S = a(1 − rⁿ)/(1 − r) for the total in row n.
  • I can add up equal yearly deposits that grow by the same percent.
  • I can tell when an infinite geometric series has a total (r between -1 and 1) and find it with a ÷ (1 − r).

Standard: A-SSE.B.4

Words to know

geometric series: A series whose terms multiply by the same ratio r each row.

ratio (r): The number each term is multiplied by: term ÷ the term before.

finite sum: The total of a set number of terms: S = a(1 − rⁿ)/(1 − r).

infinite series: A series whose terms go on forever, shown by the dots …

converges: The running total levels off at one number; it happens when -1 < r < 1.

growth factor: 1 + the rate: 4% growth multiplies by 1.04.

Common mistakes

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

Stopped one term early, using n − 1 terms. Count the terms or deposits together before using the formula.

Multiplied the running total by the ratio instead of adding the next term. Add 3 + 6 + 12 by hand and compare with 9 × 2.

What to say

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

Questions parents ask

What is the most common mistake with sum of a finite geometric series, and infinite geometric series?

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

How can I help my child with sum of a finite geometric series, and infinite geometric 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.

More algebra 2

See all Algebra 2

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records

Ready for easier practice?

Print a sheet, scan it when it’s done, and PencilGo picks the next one.

Create a free account