Worksheets · Algebra 2

Infinite geometric series worksheet

When the ratio is between -1 and 1 the terms shrink fast enough that the total settles on a number. One formula: the first term over one minus the ratio.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Infinite Geometric Series

Date Period

Find each sum.

  1. Find the sum: 15,3,35,
  2. Find the sum: 15,10,203,
  3. Find the sum: 11,112,114,
  4. Find the sum: 14,7,72,
  5. Find the sum: 13,133,139,
  6. Find the sum: 13,265,5225,
  7. Find the sum: 14,145,1425,
  8. Find the sum: 11,113,119,
  9. Find the sum: 13,134,1316,
  10. Find the sum: 15,152,154,
  11. Find the sum: 11,223,449,
  12. Find the sum: 15,12,485,
  13. Find the sum: 15,252,12512,
  14. Find the sum: 14,283,569,
  15. Find the sum: 15,152,154,
  16. Find the sum: 14,425,12625,
  17. Find the sum: 15,5,53,
  18. Find the sum: 11,113,119,
  19. Find the sum: 11,115,1125,
  20. Find the sum: 15,6,125,

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Infinite Geometric SeriesAnswer keyVersion 1

Date Period

Find each sum.

  1. Find the sum: 15,3,35,754
  2. Find the sum: 15,10,203,45
  3. Find the sum: 11,112,114,223
  4. Find the sum: 14,7,72,283
  5. Find the sum: 13,133,139,394
  6. Find the sum: 13,265,5225,657
  7. Find the sum: 14,145,1425,352
  8. Find the sum: 11,113,119,332
  9. Find the sum: 13,134,1316,525
  10. Find the sum: 15,152,154,10
  11. Find the sum: 11,223,449,33
  12. Find the sum: 15,12,485,75
  13. Find the sum: 15,252,12512,9011
  14. Find the sum: 14,283,569,42
  15. Find the sum: 15,152,154,30
  16. Find the sum: 14,425,12625,35
  17. Find the sum: 15,5,53,454
  18. Find the sum: 11,113,119,332
  19. Find the sum: 11,115,1125,554
  20. Find the sum: 15,6,125,25

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Find the sum: 12,6,3,

  1. Each term is half the one before, so r is one half.
  2. The sum is 12 over 1 minus one half.

The answer is 24.

Where students go wrong

Using the formula when the ratio is bigger than 1. A series like 2, 6, 18 grows without limit and has no sum at all, and the formula will happily give a negative number for it.

Also called sum to infinity or convergent series.

Questions about these worksheets

Yes. Every infinite geometric series sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the infinite geometric series questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Using the formula when the ratio is bigger than 1. A series like 2, 6, 18 grows without limit and has no sum at all, and the formula will happily give a negative number for it.