PAPER ONE
NUMBER PATTERNS
LINEAR: QUADRATIC:
- Constant 1st difference (a) - Constant second difference
- Tn=an+c - Tn=an2+bn+c
2a = constant 2nd difference
3a+b = first 1st difference
a+b+c = T1
ARITHMETIC: GEOMETRIC:
- Constant difference (d) - Constant ratio (r)
𝑇 𝑇
- T2-T1=T3-T2 - 𝑇2 = 𝑇3
1 2
- Tn=a+(n+1)d
- Tn = a.rn-1
- First term: a
SEQUENCE → separated by semi-colons SUM TO INFINITY:
SERIES → separated by addition signs
𝑎
𝑆∞ = 1−𝑟 the series converges here
𝑛
𝑆𝑛 = 2 [2𝑎 + (𝑛 − 1)𝑑] ∗ −1 < 𝑟 < 1
𝑎(𝑟 𝑛 − 1)
𝑆𝑛 =
𝑟 −1
*𝑆𝑛−1 = 𝑇1 + 𝑇2 + 𝑇3 + ⋯ + 𝑇𝑛−1
∴ 𝑆𝑛 − 𝑆𝑛−1 = 𝑇𝑛
SIGMA NOTATION:
*If the ‘start’ is 1, then n = ‘end’
If the ‘start’ is not 1, then n = ‘end’ – ‘start’ +1
End
Start
*’expand’ = write out with + between terms (one mark)
‘evaluate’/’determine’ = add all the terms together
NUMBER PATTERNS
LINEAR: QUADRATIC:
- Constant 1st difference (a) - Constant second difference
- Tn=an+c - Tn=an2+bn+c
2a = constant 2nd difference
3a+b = first 1st difference
a+b+c = T1
ARITHMETIC: GEOMETRIC:
- Constant difference (d) - Constant ratio (r)
𝑇 𝑇
- T2-T1=T3-T2 - 𝑇2 = 𝑇3
1 2
- Tn=a+(n+1)d
- Tn = a.rn-1
- First term: a
SEQUENCE → separated by semi-colons SUM TO INFINITY:
SERIES → separated by addition signs
𝑎
𝑆∞ = 1−𝑟 the series converges here
𝑛
𝑆𝑛 = 2 [2𝑎 + (𝑛 − 1)𝑑] ∗ −1 < 𝑟 < 1
𝑎(𝑟 𝑛 − 1)
𝑆𝑛 =
𝑟 −1
*𝑆𝑛−1 = 𝑇1 + 𝑇2 + 𝑇3 + ⋯ + 𝑇𝑛−1
∴ 𝑆𝑛 − 𝑆𝑛−1 = 𝑇𝑛
SIGMA NOTATION:
*If the ‘start’ is 1, then n = ‘end’
If the ‘start’ is not 1, then n = ‘end’ – ‘start’ +1
End
Start
*’expand’ = write out with + between terms (one mark)
‘evaluate’/’determine’ = add all the terms together
