Sequences & Series

Formulas are organized based on their importance in the CAT exam.
1 Arithmetic-Geometric Series Sum
2 Geometric Mean (GM) of n Numbers
3 Sum of Squares of First n Natural Numbers
4 Recurrence for an AP
5 Last Term of an AP
6 Sum of First n Odd Natural Numbers
7 Sum of First n Natural Numbers
8 Geometric Progression in Terms of Two Terms
9 Sum of a Binomial Expansion
10 Arithmetic Mean
11 AM-GM for Multiple Positive Numbers
12 Monotonicity of a GP
13 Arithmetic Progression in Terms of Two Terms
14 Geometric Progression: Sum to Infinity
15 Geometric Progression
16 Middle Term of a GP
17 Relation Between AM, GM and HM
18 Sum of a Finite Geometric Series in Alternative Form
19 Relation Between AM and HM
20 Convergence of a GP
21 Sum of an AP
22 Sum of a GP Starting from the $$m$$th Term
23 Geometric Mean of Terms of a GP
24 Sum of Terms in a GP with General Starting Index
25 Four Numbers in AP
26 Sum of a GP Using First and Last Terms
27 Common Ratio of a GP
28 Sum of Consecutive Odd Numbers
29 Middle Term of an AP
30 Three Numbers in AP and GP
31 Sum of First $$n$$ Even Numbers
32 Sequence
33 Three Numbers in GP
34 Harmonic Progression
35 Common Difference
36
37 Recurrence for a GP
38 Harmonic Mean
39 Geometric Mean
40 Inserting Geometric Means
41 Sequence Defined by a Recurrence
42 Inserting Arithmetic Means
43 Arithmetic Mean of Terms of an AP
44 Infinite GP with Alternating Terms
45 Relation Between Equidistant Terms of an AP
46 Properties of an AP
47 Sum of Reciprocals of Consecutive Products
48 Average of Terms in an Arithmetic Progression
49 Sum of First $$n$$ Odd Numbers
50 Infinite Geometric Progression
51 Sum of Consecutive Integers from $$m$$ to $$n$$
52 Sum of a Finite GP
53 Infinite GP Remainder
54 Infinite Arithmetic-Geometric Progression
55 Relation Between Equidistant Terms of a GP
56 Sum of Fourth Powers
57 Sum of Squares of First $$n$$ Natural Numbers
58 Partial Fractions in Telescoping Sums
59 Sum of a General Linear Sequence
60 Weighted Binomial Sum
61 Sum of Cubes of First $$n$$ Natural Numbers
62 Sum of Consecutive Even Numbers
63 Sum of Fourth Powers
64 Change of Index in Summation
65 Telescoping Series
66 Arithmetic Mean–Geometric Mean Relation
67 Sum of Binomial Coefficients
68 Sum of Products of Consecutive Natural Numbers
69 Monotonicity of an AP
70 Arithmetic Progression
71 Geometric Progression: Sum of n Terms (Finite)
72 Last Term of a GP
73 Sum of First $$n$$ Natural Numbers
74 Arithmetic-Geometric Progression
75 Sigma Notation
76 Arithmetic Progression: Sum of n Terms
77 Geometric Progression: General Term
78 Arithmetic Mean (AM) of n Numbers
79 Arithmetic Progression: General Term
80 Infinite GP as a Limit
81 Sum of Terms in an AP with General Starting Index
82 Sum of a Binomial Expansion
83 Telescoping Series: Partial Fractions Example
84 Harmonic Progression: Definition
85 Harmonic Mean (HM) of n Numbers
86 Sum of Cubes of First n Natural Numbers
87 Three Numbers in AP