Definitions [5]
An Arithmetic Progression (A.P.) is a sequence in which the difference between consecutive terms is constant.
- Common difference = d = second term − first term
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The general form of an AP is a, a + d, a + 2d, a + 3d, …
a = first term
d = common difference
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)
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.
Formulae [1]
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
