Algebra 2 - Arithmetic Sequences Flashcards

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@EnthralledSaxhorn

Study Notes

Arithmetic Sequences Overview

An arithmetic sequence is defined by a common difference (d) between consecutive terms.

Common Differences

An arithmetic sequence with a common difference of d=4 includes the terms: -13, -9, -5, -1, 3.
An arithmetic sequence with a common difference of d=-4 features the terms: 13, 9, 5, 1, -3.

Finding Sequence Terms

For the arithmetic sequence represented by aₙ=-10-3n, the first five terms are: -13, -16, -19, -22, -25.
The sequence aₙ=10+3n yields the first five terms: 13, 16, 19, 22, 25.
The sequence aₙ=8+5n gives the first five terms: 13, 18, 23, 28, 33.
In the case of aₙ=-8-2n, the first five terms are: -10, -12, -14, -16, -18.

Explicit Formulas

The explicit formula for an arithmetic sequence starting with a₁=3 and a common difference of d=7 is aₙ=-4+7n.
For a sequence with a₁=7 and d=3, the formula is aₙ=4+3n.
If a₁=5 and d=8, the formula becomes aₙ=-3+8n.
For a₁=8 and d=5, the formula is aₙ=3+5n.

Finding Missing Terms

In the sequence 10, __, __, __, __, __, 40, the missing terms are: 15, 20, 25, 30, 35.
For the sequence -17, __, __, __, __, __, -35, the missing terms include: -20, -23, -26, -29, -32.

Description

Test your understanding of arithmetic sequences with these flashcards. Each card focuses on identifying common differences and finding terms of specific sequences. Perfect for reviewing key concepts in Algebra 2.