Arithmetic/Geometric Sequences and Series Flashcards
1
Q
Difference between terms in an AP
A
Tn - Tn-1
2
Q
A sequence is called an AP if…
A
Tn-Tn-1=d for all n>2
3
Q
Tn= (AP)
A
Tn-1+d
4
Q
The nth term of an AP=
A
a + (n-1) x d
5
Q
ratio of a GP=
A
Tn/Tn-1 = r
6
Q
Tn= (GP)
A
Tn-1 x r
7
Q
The nth term of a GP=
A
ar^n-1
8
Q
Three numbers a, b and c form an AP if…
A
b-a = c-b (same common difference)
9
Q
Three numbers a, b and c form a GP if…
A
b/a = c/b (same common ratio)
10
Q
Sn =
A
T1 + T2 + T3 + … +Tn
11
Q
Tn= (Sn)
A
Tn = Sn - Sn-1 for n>2
12
Q
How to find the sum of an AP
A
Sn = 1/2 n(a+l) --> when the last term l is known Sn = 1/2 n(2a +(n-1)d)
13
Q
How to find the sum of a GP
A
When r>1: Sn = a(r^n-1)/r-1
When r<1: Sn = a(1-r^n-1)/1-r
14
Q
How to find the limiting sum of a GP
A
If -1
15
Q
How to convert a recurring decimal to a fraction
A
Write the recurring part as a GP then find S∞
e.g 0.27272727… = 0.27 + 0.0027 +…
