Understanding sequences in mathematics is essential for recognizing patterns and solving problems. This overview distinguishes between arithmetic sequences, with a constant difference between terms, and geometric sequences, which have a constant ratio. It explains how to use term-to-term and position-to-term rules for finding specific terms in a sequence, highlighting the practical applications of these methods in various fields.
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Sequences are an ordered list of numbers that follow a particular pattern or rule
Predicting subsequent terms
Understanding the pattern in a sequence is crucial for predicting subsequent terms
Practical applications
The pattern in a sequence has practical applications, such as in financial planning
Sequences can be classified as arithmetic or geometric
An arithmetic sequence has a constant difference between consecutive terms, known as the common difference
The term-to-term rule involves adding the common difference to the current term to find the next term in an arithmetic sequence
The position-to-term rule allows for the direct calculation of any term in an arithmetic sequence using a formula
A geometric sequence has a constant ratio between successive terms, known as the common ratio
The term-to-term rule involves multiplying the current term by the common ratio to find the next term in a geometric sequence
The position-to-term rule allows for the direct calculation of any term in a geometric sequence using a formula
Sequences are useful in financial planning, such as modeling salary increases over time
Mastery of term generation in sequences is a critical mathematical skill with wide-ranging applications, including problem-solving in various disciplines
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A person's salary progression, starting at £______ with an annual increase of £______, can be represented as a mathematical ______.
27,000
1,000
sequence
01
Definition of arithmetic sequence
Sequence with constant difference between terms, called common difference.
02
Example of arithmetic sequence
Sequence 2, 5, 8, 11, 14 with common difference of 3.
