← Algebra I

Unit 8: Sequences

A sequence is a function whose inputs are the counting numbers -- arithmetic sequences add the same amount each step, geometric ones multiply.

4 topics · 13 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Arithmetic Sequences

  1. How it worksHow does a constant common difference define every arithmetic sequence?
  2. Worked exampleFind the next three terms of the arithmetic sequence 4, 9, 14, 19.
  3. Common mistakeWhy isn't a sequence arithmetic just because its terms are getting bigger?
  4. Going furtherWhat happens to an arithmetic sequence when its common difference is negative?
Your turn1 of 2
An arithmetic sequence starts at 7 with a common difference of 7. Write a formula for its nth term, a(n).

Writing Rules for Arithmetic Sequences

  1. How it worksHow does the common difference and the first term combine into an explicit formula for any term?
  2. Worked exampleFind the 20th term of the arithmetic sequence that starts 7, 11, 15, 19.
  3. Ties togetherHow does the formula for an arithmetic sequence connect to the slope-intercept form of a line?
Your turn1 of 2
An arithmetic sequence starts 7, and has common difference 7. Find its nth term, as a function of n.

Geometric Sequences

  1. How it worksHow does a constant common ratio define every geometric sequence?
  2. Worked exampleFind the next three terms of the geometric sequence 3, 6, 12, 24.
  3. Common mistakeWhy isn't a sequence geometric just because each term is bigger than the last?
Your turn1 of 2
A geometric sequence starts at 4 with a common ratio of 3. Write a formula for its nth term, a(n).

Writing Rules for Geometric Sequences

  1. How it worksHow does the common ratio and first term build an explicit formula for the nth term?
  2. Worked exampleFind the 8th term of the geometric sequence that starts 2, 6, 18, 54.
  3. Ties togetherHow does a geometric sequence's formula connect to exponential growth functions?
Your turn1 of 2
A geometric sequence starts at 4 with common ratio 3. Find its nth term, as a function of n.