Mathematics Specification A - 4MA1 PearsonEdexcel

Sequences

Gbogbo ọrọ náà

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.

Ebumnobi

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)

Akọmọ Ojú-ẹkọ

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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Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Sequences. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

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