Covers the various sections relating to Patterns, Sequences and Series within the Mathematics syllabus. (Paper 1 section) Includes notes from the textbook, as well as...
Tn = an + b
Common difference = a
Sub one value and it’s n into equation and solve = b
Quadratic
(2nd difference constant)
Tn = an2 + bn + c
Common difference = 2a
T0 = c
Sub in a and c, but in value and it’s n into equation and solve = b
Cubic
(3rd difference constant)
Tn = an3 + bn2 + cn + d
, Arithmetic Sequences
e.g. 2; 5; 8; 11; 14; …
Constant difference = d
d = Tn – Tn-1
. = T2 – T1
. = T3 – T2
Linear formula:
T1 = a
T2 = a + d
T3 = a + 2d
Tn = a + (n – 1) d
Type 1: Find the value of a term
Determine the 30th term of the sequence 45; 50; 55; …
Tn = a + (n – 1) d
a = 45
d=5
T30 = 45 + (30 – 1) 5
. = 190
Type 2 : Find the number of terms
How many terms are there in the sequence 13; 10; 7; …; - 44
Tn = a + (n – 1) d
a = 13
d=-3
-44 = 13 + (n – 1) - 3
. n = 20
Type 3: Find the sequence
Find the sequence if the 10th term is 31 and the 15th term is 46
31 = a + (10 – 1) d 46 = a + (15 – 1) d
31 = a + 9d 46 = a + 14d
. a = 31 – 9d . a = 46 – 14d
31 – 9d = 46 – 14d a = 31 – 9(3)
d=3 a=4
Tn = 4 + (n – 1) 3
4; 7; 10; …
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller KirstenBarbour. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.16. You're not tied to anything after your purchase.
