Definitions [4]
When the numbers (terms) in a sequence are connected to each other by a positive (plus) sign or a negative (minus) sign, the sequence becomes a series.
A progression is a sequence where each term follows a uniform rule.
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Every progression is a sequence, but with a clear pattern.
A sequence is a group of numbers arranged in a definite order following a rule.
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Numbers in a sequence are called terms or elements.
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The term at position n is called the nth term, denoted by Tₙ.
A sequence, in which each of its terms can be obtained by multiplying or dividing its preceding term by a fixed quantity, is called a geometric progression.
- A fixed number is called the common ratio (r)
Formulae [2]
If r < 1→ use \[S_n=\frac{a(1-r^n)}{1-r}\]
If r > 1 → use \[S_n=\frac{a(r^n-1)}{r-1}\]
If r = 1 → Sn = na
If r < 1→ use \[S_n=\frac{a(1-r^n)}{1-r}\]
If r > 1 → use \[S_n=\frac{a(r^n-1)}{r-1}\]
If r = 1 → Sn = na
Concepts [9]
- Sequence, Series, and Progression
- Geometric Progression (G. P.)
- General Term Or the nth Term of a G.P.
- Sum to' n' Terms of a Geometric Progression
- Sum to' n' Terms of a Geometric Progression
- Recurring Decimals
- Harmonic Progression (H. P.)
- Types of Means
- Special Series (Sigma Notation)
