Sequences and Series

A sequence is an ordered arrangement

A sequence is an ordered arrangement of numbers following a specific pattern or rule. It can be viewed as a function whose domain is natural numbers.

A series is the sum

A series is the sum of terms of a sequence, expressed as a₁ + a₂ + a₃ + ... + aₙ. It can be written in sigma notation as Σaₖ. Like sequences, series c

A geometric progression is a sequence

A geometric progression is a sequence where each term (except the first) is obtained by multiplying the previous term by a constant called the common

For a G

For a G.P. with first term 'a' and common ratio 'r': If r = 1, then Sₙ = na. If r ≠ 1, then Sₙ = a(rⁿ - 1)/(r - 1) or Sₙ = a(1 - rⁿ)/(1 - r). This for

The geometric mean of two positive

The geometric mean of two positive numbers a and b is √(ab). For n numbers between a and b forming a G.P., each geometric mean can be calculated using