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Sequences | O Level Mathematics 4024 & IGCSE Mathematics 0580 | Detailed Free Notes To Score An A Star (A*)

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  • It is a hard chapter when it comes in A level, but here the concept is very simple
  • A sequence is a group of numbers where you can predict the next value due to the pattern in the group
    • Either something will be adding to the entire group
    • For example 0,2,4,6,8 it means that we are adding 2 in each step, so the next value will be 10,12,14 and so on
    • We can be subtracting a number, for example 10,9,8,7, which means one number is being deducted in each stage, which means that the next few values will be 6,5,4 and so on.
    • We can be multiplying something
      • For example 2,4,8,16, here we are multiplying by 2
    • Or we can be dividing
      • 32,16,8,4
        • Here we are dividing by 2
  • The real issue comes in the exams where he will give you a sequence and would ask you to make another sequence based on the sequence you just built.
    • For the sequences where we are either adding or subtracting, we can use the general arithmetic formula
      • nth term = first term + difference in each term (nth term -1)
      • In other words n= a+d(n-1)
  • Another situation can be where the difference is increasing in each step as well
    • For example
      • 2,3,5,8,12
      • First, let us see the difference between each term
      • 2=3 means 1 was added
      • 3= 5 means 2 was added
      • 5 = 8 means 3 was added
      • 8 =12 means 4 was added
    • Here, the general formula is as follows
      • First, we use the same formula as above
      • a+d(n-1)
      • Next we add the following
      • + c(n-1)(n-2)/2
      • So the complete formula is
      • a+d(n-1) + [c(n-1)(n-2)/2]
  • That’s the tricky part
    • Sometimes, what he will do in the exam is, he will provide you a sequence and its formula,
    • Then, he will give you another sequence, where it is super hard to create the formula yourself and ask for its formula
    • The trick is, just check what is the difference between the terms of the first sequence where the formula is given, and the sequence you need to find the formula for.
    • For example, if the first term of the sequence he gave you with the formula and the first term of the sequence you need to find the formula of has a difference of +5, just add 5 to the formula of the first equation and that is formula for the second one.
    • So if the formula for the first sequence, that he already gave, was 24+6n-d^2, the formula for the second sequence would be 24+6n-d^2+5 or
    • 29+6n-d^2
  • No other rocket science in this chapter as well
Hunain Zia

Hunain Zia has previously achieved considerable success in the high-school educational stream, gaining a massive 154 Total A Grades and 7 Major Distinctions, a process in which he broke/ set 11 different world records, including the most A grades ever achieved, most subjects ever appeared in, most distinctions, gaining distinctions across two separate boards (Pearson Edexcel and CAIE) within the same year/ ever, and even 19 hours of constant examination. All records stand intact today. Hunain pursued his Honors Accounting Degree from the prestigious Bentley University, and then completed an LLB (in Honors) from University of London. Currently, he manages multiple social and commercial projects, has founded digital streams and works tirelessly in the education sector.

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