Arithmetic Sequences

Learn and apply arithmetic sequences using equations, examples, and interpretation.

Lesson 5 of 53 parts Practice Flashcards

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Common Difference

Objective: Explain and use common difference in an Algebra 1 problem.

An arithmetic sequence changes by a constant difference from one term to the next. The terms decrease at a constant step.

Worked examples

Try itExample 1.1: A sequence starts at 13 and adds 2 each time. What is term 6?Show answer

23. Take 5 equal steps of size 2 after the first term. The answer is 23.

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Objective: Explain and use common difference in an Algebra 1 problem.

An arithmetic sequence changes by a constant difference from one term to the next. The terms decrease at a constant step.

Worked examples

Try itExample 1.1: A sequence starts at 13 and adds 2 each time. What is term 6?Show answer

23. Take 5 equal steps of size 2 after the first term. The answer is 23.

Objective: Explain and use explicit rule in an Algebra 1 problem.

For first term a₁ and common difference d, the nth term is aₙ=a₁+(n−1)d for positive integer n. The first term is zero steps after itself.

Worked examples

Try itExample 2.1: A sequence starts at 23 and adds 3 each time. What is term 9?Show answer

47. Take 8 equal steps of size 3 after the first term. The answer is 47.

Objective: Explain and use recursive rule in an Algebra 1 problem.

A recursive rule gives a starting term and a rule such as aₙ=aₙ₋₁+d to find the next term. An initial term to start the sequence.

Worked examples

Try itExample 3.1: A sequence starts at 33 and adds 4 each time. What is term 12?Show answer

77. Take 11 equal steps of size 4 after the first term. The answer is 77.

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