Help your students prepare for their Maths GCSE with this free sequences worksheet of 30+ questions and answers
Sequences are a set of numbers that have a starting number and go on forever. Number sequences can increase or decrease and can be whole numbers, fractions or decimals.
There are different ways to classify a sequence including arithmetic sequences and geometric sequences. Arithmetic sequences have a common difference and geometric sequences have a common ratio. The common difference or common ratio can be used to continue a sequence, or to find missing terms within the sequence and may be referred to as the term-to-term rule.
Arithmetic sequences are based on multiples which can be used to find the nth term rule (or nth term formula) by calculating the common difference by subtracting two consecutive terms in the sequence. The common difference gives the coefficient of the n in the nth term formula.
The nth term can be referred to as the position-to-term rule and can be used to find a particular term in the sequence or used to check if a particular value is in the sequence or not. A sequence that is increasing or decreasing by the same amount is called a linear sequence.
There are other types of sequences such as the square numbers that form a sequence which is involved in quadratic sequences. Other non-linear sequences include the cube numbers and the powers of 10. There is also the Fibonacci sequence where the next term is found by adding the previous two terms. Triangular numbers is another special sequence which is useful to know.
Looking forward, students can progress with other sequences worksheets and on to additional algebra worksheets, for example a simplifying expressions worksheet, straight line graph or simultaneous equations worksheet.
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