Sequences

Definition of Sequences

• A sequence is a set of numbers, or terms, arranged in a specific order.
• The position of each term in the sequence is called its index or rank.
• In sequences, the nth term represents any term number in the sequence.
• There are different types of sequences, including arithmetic sequences, geometric sequences and fractional sequences.

Finding the Nth Term

• To find the nth term of an arithmetic sequence, first find the common difference - the amount that each term increases by.
• The formula for the nth term in an arithmetic sequence is an + b, where ‘a’ is the common difference and ‘b’ is the first term subtracted from the common difference.

Arithmetic and Geometric Sequences

• In an arithmetic sequence, each term is found by adding the same value each time. The value added is called the common difference.
• In a geometric sequence, each term is found by multiplying by the same value each time - this is called the common ratio.
• The formula for the nth term in a geometric sequence is ar^(n-1), where ‘a’ is the first term and ‘r’ is the common ratio.

Fractional Sequences

• A fractional sequence is a sequence where the nth term is given by a fraction.
• In a fractional sequence, the numerator and the denominator often follow separate arithmetic or geometric sequences.

Common Mistakes with Sequences

• Calculating the nth term incorrectly is a common mistake. Make sure to use the correct formula depending on the type of sequence.
• Mixing up arithmetic and geometric sequences. Remember, arithmetic sequences involve addition or subtraction, whilst geometric sequences involve multiplication or division.
• Forgetting to reduce fractions to their simplest form in fractional sequences. Always simplify fractions where possible.