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Patterns, Sequences, Series and Logic

Sequences and series, patterns, repeating cycles, and the logic and flowcharts E3n names in its own description of the Algebra and Other Math sub-score.

5 topics · 20 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.

Patterns and Finding the Rule

  1. How it worksHow do you test a candidate rule against every term instead of just the first two?
  2. Worked exampleFind the next two terms of 3, 7, 15, 31, 63 and state the rule that builds them.
  3. Worked exampleWalk me through the pattern behind 1, 4, 9, 16, 25 and find its 12th term.
  4. Going furtherWhat changes about finding the rule when a pattern is built from dots and shapes instead of numbers?
Your turneasy1 of 3
A pattern starts at 7 and each term after that is double the term before it plus 1. What is the fourth term?

Arithmetic Sequences

  1. How it worksHow does the common difference let you leap to the 50th term without writing out the first 49?
  2. Worked exampleFind the 40th term of 7, 11, 15, 19 using the common difference.
  3. Worked exampleWalk me through counting how many terms sit in the list 5, 9, 13, all the way up to 101.
  4. Common mistakeWhy isn't the 10th term of an arithmetic sequence just ten times the first term?
  5. Ties togetherHow does the common difference of a sequence show up as the slope of a line through its terms?
Your turneasy1 of 3
An arithmetic sequence starts at 9 and has a common difference of 7. Write an expression for term number n, in terms of n.

Geometric Sequences and Series

  1. How it worksHow does a common ratio push a sequence forward by multiplying and backward by dividing?
  2. Worked exampleFind the 7th term of 3, 6, 12, 24 and then the sum of all seven of those terms.
  3. Common mistakeWhy isn't 2, 6, 18 an arithmetic sequence when its gaps grow by a perfectly good rule?
  4. Going furtherWhat happens to a geometric sequence once the common ratio is a fraction such as 1/2?
Your turneasy1 of 3
A geometric sequence starts at 5 and has a common ratio of 3. Write an expression for term number n, in terms of n.

Repeating Cycles and Remainders

  1. How it worksHow does dividing the position by the length of the cycle tell you where in the loop you land?
  2. Worked exampleFind the units digit of 3 raised to the 47th power using its four-step cycle.
  3. Worked exampleWalk me through finding the 100th letter in the endlessly repeating block A B C D E.
Your turneasy1 of 3
A block of 7 letters repeats endlessly. How many letters have gone by at the end of 29 complete blocks?

Logic and Flowcharts

  1. How it worksHow does a flowchart turn a rule full of branches into a single path you can walk?
  2. Worked exampleWalk me through a flowchart that doubles a number if it is even and adds 3 if it is odd, starting at 7.
  3. How it worksHow do two overlapping circles show which claims about two groups of people have to be true?
  4. Common mistakeWhy doesn't knowing the game was cancelled tell you it rained, when rain always cancels the game?
Your turneasy1 of 3
On item 17 a student reads all squares are rectangles as meaning all rectangles are squares. What does the first statement actually say?

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