Arithmetic & Geometric Sequences Worksheets


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Arithmetic & Geometric Sequences

Examples, solutions, videos, and worksheets to help Grade 8 students learn how to find the terms of an Arithmetic & Geometric Sequence. Identify whether a sequence is an Arithmetic or Geometric sequence. Write a recursive formula for the sequence.

Arithmetic & Geometric Sequences

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is called the common difference and is often denoted by 𝑑.

Formula for the 𝑛-th Term
For an arithmetic sequence with first term π‘Ž and common difference 𝑑, the 𝑛-th term π‘Žπ‘› can be calculated by:

π‘Žπ‘› = π‘Ž + (𝑛 βˆ’ 1)𝑑
π‘Ž: The first term of the sequence.
𝑑: The common difference.
𝑛: The term number you’re looking to find.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio π‘Ÿ.

Formula for the 𝑛-th Term
For a geometric sequence with the first term π‘Ž and common ratio π‘Ÿ, the 𝑛-th term π‘Žπ‘› is calculated as:

π‘Žπ‘› = π‘Ž Γ— π‘Ÿ(𝑛 βˆ’ 1)
π‘Ž: The first term of the sequence.
π‘Ÿ: The common ratio.
𝑛: The term number you want to find.

Have a look at this video if you need to review Arithmetic & Geometric Sequences.

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Arithmetic & Geometric Sequences Worksheets
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Arithmetic & Geometric Sequences

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