Arithmetic & Geometric Sequences Worksheets

Printable & Online “Sequences” worksheets:
Find the sequence & n^th term
Find the sequence & n^th term
Find the n^th term of a sequence with fractions
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 𝑎 and common difference 𝑑, the 𝑛-th term 𝑎_𝑛 can be calculated by:

𝑎𝑛 = 𝑎 + (𝑛 − 1)𝑑
𝑎: 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 𝑟.

Formula for the 𝑛-th Term
For a geometric sequence with the first term 𝑎 and common ratio 𝑟, the 𝑛-th term 𝑎_𝑛 is calculated as:

𝑎_𝑛 = 𝑎 × 𝑟^{(𝑛 − 1)}
𝑎: The first term of the sequence.
𝑟: 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.

• Arithmetic & Geometric Sequences

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