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- 1.1 Standard Form.
- 1.2 Arithmetic sequences and series.

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Matchstick Patterns Create a formula to describe the nth term of a sequence by examining the structure of the diagrams.
- Standard Form Test your understanding of standard form (scientific notation) with this self-marking quiz.
- Standard Form Video Learn how to write and calculate with numbers in standard form - sometimes called scientific notation.
- Standard Order Arrange the numbers given in standard form with the smallest at the top and the largest at the bottom.
- Arithmetic Sequences An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.
- Arithmetic Sequences Video A reminder of how to find the next term, the nth term and the sum of terms of an arithmetic or linear sequence.
- Venn Diagram of Sequences Find the formula for the nth term of sequences that belong in the given sets.
- Sequences Table Challenge Complete the table showing the terms of the sequences and the formulas for the nth terms.
- Parts of Sequences Find the formula that describes the part of the sequence that can be seen
- Sigma Practise using the sigma notation to find the sum of various number series.

Here are some exam-style questions on this topic:

- "
*(a) Write 0.0000657 in standard form.*" ... more - "
*(a) Find the \(n\)th term of the sequence 7, 13, 19, 25,...*" ... more - "
*The following table shows the distance from the sun and mass of the eight planets.*" ... more - "
*At a particular time the distance between Earth and Mercury was \(7.7 \times 10^7\) km.*" ... more - "
*The Moon appears to orbit around the Earth with an average radius of 385 thousand kilometres.*" ... more - "
*The volume of the Moon is \(2.2 \times 10^{10}\) km*" ... more^{3} - "
*The surface gravity, \(g\), of a planet is the gravitational acceleration experienced at its surface. The following formula can be used to find how a planet's gravity compares to Earth's.*" ... more - "
*The first three and last terms of an arithmetic sequence are \(7,13,19,...,1357\)*" ... more - "
*An arithmetic sequence is given by 6, 13, 20, …*" ... more - "
*In an arithmetic sequence, the fifth term is 44 and the ninth term is 80.*" ... more - "
*NASA’s Transiting Exoplanet Survey Satellite (TESS) has discovered a planet between the sizes of Mars and Earth orbiting a bright, cool, nearby star. The planet, called L 98-59b, marks the smallest found by TESS yet. The radius of L 98-59b is \(5.42\times 10^6\) m.*" ... more - "
*A celebrity football match is planned to take place in a large stadium.*" ... more - "
*A Grecian amphitheatre was built in the form of a horseshoe and has 22 rows.*" ... more - "
*Consider an arithmetic sequence where \(u_{10}=S_{10}=15\). Find the value of the first term, \(u_1\) and the value of the common difference, \(d\).*" ... more - "
*(a) Expand the following as the sum of six terms:*" ... more - "
*Consider the number sequence where \(u_1=500, u_2=519, u_3=538\) and \(u_4=557\) etc.*" ... more

Here is an Advanced Starter on this statement:

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Indices Where do many fish live? Indices (in the seas!) This topic involves the use of the index, power or exponent. The concept is easily misunderstood and a surprisingly large number of pupils will evaluate 62 as 12 and not 36. After having mastered positive integer indices pupils should move on to negative indices and fractional indices. Exploring this topic in both numeric and algebraic ways will provide understanding and competence in this important concept.
- Sequences A pattern of numbers following a rule is called a sequence. There are many different types of sequence and this topic introduces pupils to some of them. The most basic sequences of numbers is formed by adding a constant to a term to get the next term of the sequence. This rule can be expressed as a linear equation and the terms of the sequence when plotted as a series of coordinates forms a straight line. More complex sequences are investigated where the rule is not a linear function. Other well-known sequences includes the Fibonacci sequence where the rule for obtaining the next term depends on the previous two terms. Sequences can be derived from shapes and patterns. A growing patterns of squares or triangles formed from toothpicks is often used to show linear sequences in a very practical way. Diagrams representing sequences provides interesting display material for the classroom. Typically pupils are challenged to find the next term of a given sequence but a deeper understanding is needed to find intermediate terms, 100th term or the nth term of a sequence.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.