- A sequence is an arrangement of numbers in a definite order according to some rule.
- If is a sequence, is the corresponding series.
- If the number of terms in a sequence or series is finite, we call it a finite sequence (series), otherwise it is infinite sequence (series).
- If an Arithmetic Progression (A.P), every term either increases or decreases by a fixed quantity called the common difference.
If is the term and , the common differences,
where is the number of terms;
- In a geometric progression (G.P) every term is either multiplied or divided by a fixed non-zero quantity to get the next term. This quantity is called the common ratio.
- If is the term and the common ratio, then
where a and b are the numbers between which G.M found.
- A harmonic progression (H.P) is formed by the reciprocals of an A.P.
forms a H.P
H.M between = .
- If A, G, H are the A.M, G.M and H.M between any two numbers, then
- Miscellaneous series:
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