Mathematics Specification A - 4MA1 PearsonEdexcel

Sequences

Bayani Gaba-gaba

A sequence is an ordered list of numbers that follows a rule. You meet sequences everywhere in mathematics: the multiples of 7, the square numbers, the Fibonacci numbers. On the Edexcel IGCSE, you need to continue a sequence from a given rule, spot the pattern in a sequence of integers, and write an expression for the nth term of an arithmetic (linear) sequence.

This lesson starts with term-to-term rules (where each term depends on the one before) and position-to-term rules (where each term depends on its position number). You will then learn how to find the nth-term formula for arithmetic sequences by inspection and, at Higher tier, use the formal notation \(a + (n - 1)d\) and the sum formula for arithmetic series.

Manufura

Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence
Find subsequent terms of an integer sequence and the rule for generating it
Use linear expressions to describe the nth term of arithmetic sequences
[Higher] Understand and use common difference (d) and first term (a) in an arithmetic sequence
[Higher] Know and use nth term = a + (n - 1)d
[Higher] Find the sum of the first n terms of an arithmetic series (Sn)

Takardar Darasi

Suppose you save money each week. In week 1 you save 5 pounds, in week 2 you save 10 pounds, in week 3 you save 15 pounds, and so on. The amounts 5, 10, 15, 20, ... form a sequence. Each number in the list is called a term. The first term is written \(T_1\) (or \(a\)), the second \(T_2\), and the \(n\)th term \(T_n\). Finding a rule that generates the sequence lets you jump straight to any term without listing every one before it.

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Nazarin Darasi

Barka da kammala darasi akan Sequences. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.

Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.

Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.

The nth term of a sequence is 3n + 5. What is the 10th term? A) 30 B) 35 C) 38 D) 40 Answer: B
Which of these sequences is arithmetic? A) 1, 4, 9, 16, ... B) 2, 6, 18, 54, ... C) 5, 9, 13, 17, ... D) 1, 1, 2, 3, 5, ... Answer: C
The first term of a sequence is 8 and the common difference is -3. What is the 4th term? A) 2 B) -1 C) 5 D) 20 Answer: B
The nth term of a sequence is 5n - 2. Which term has the value 48? A) 8th B) 9th C) 10th D) 11th Answer: C
A sequence starts 6, 10, 14, 18, ... What is the common difference? A) 2 B) 3 C) 4 D) 6 Answer: C