Arithmetic Sequences That Count Down

Start with Arithmetic or Geometric to build the idea, then move to the arithmetic and geometric practice sheets. Use the mixed review sheets, the card sort and the mazes for review, since students can check their own paths before the answer key.

Extend 13 decreasing arithmetic sequences by two terms and name the step, like 455, 416, 377, 338. The directions on the page read: Each arithmetic sequence counts down by the same amount every time. Write the next two terms. Then write the amount that is subtracted each time. The page opens with a worked example, and an answer key is included.

Yes, both. We made it for 7th grade algebra, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Compare each term with the one before it. If you add or subtract the same number each time, the sequence is arithmetic. If you multiply by the same number each time, it is geometric. Arithmetic or Geometric gives 18 sequences to sort this way.

It is the number added to each term of an arithmetic sequence to get the next term. In 39, 53, 67, 81 the common difference is 14. Find the Next Terms in Arithmetic Sequences has students find it and write the next two terms.

It is the number each term of a geometric sequence is multiplied by to get the next term. In 17, 51, 153, 459 the common ratio is 3. When a geometric sequence shrinks, each term is divided instead, as on Geometric Sequences That Halve.

Use the first term plus (n minus 1) times the common difference. For 3, 11, 19, 27 the 20th term is 3 + 19 times 8, which is 155. Find the 10th and 20th Terms practices this with 8 sequences.