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A geometric sequence (aka Geometric Progression or GP) is one where each term is the previous term multiplied by a constant (the common difference)
As division is the inverse of multiplication, each term can also be said to be the previous term divided by the reciprocal of the constant.
The sum Sn of n terms of a GP can be found by:
Sn = a(1 - rⁿ)/(1 - r) = a(rⁿ - 1)/(r - 1)
where:
a is the first term
r is the common difference
n is the number of terms
If the value of the common difference is between -1 and 1 (ie |r| < 1), then the sum of the GP will be finite since as n→ ∞ so rⁿ → 0, and will be:
S = a/(1 - r)
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What does geometric sequence?
You mean what IS a geometric sequence? It's when the ratio of the terms is constant, meaning: 1, 2, 4, 8, 16... The ratio of one term to the term directly following it is always 1:2, or .5. So like, instead of an arithmetic sequence, where you're adding a specific amount each time, in a geometric sequence, you're multiplying by that term.
Is geometric sequence a sequence in which each successive terms of the sequence are in equal ratio?
Yes, that's what a geometric sequence is about.
Is a geometric progression a quadratic sequence?
A geometric sequence is : a•r^n while a quadratic sequence is a• n^2 + b•n + c So the answer is no, unless we are talking about an infinite sequence of zeros which strictly speaking is both a geometric and a quadratic sequence.
What is descending geometric sequence?
A geometric sequence is a sequence where each term is a constant multiple of the preceding term. This constant multiplying factor is called the common ratio and may have any real value. If the common ratio is greater than 0 but less than 1 then this produces a descending geometric sequence. EXAMPLE : Consider the sequence : 12, 6, 3, 1.5, 0.75, 0.375,...... Each term is half the preceding term. The common ratio is therefore ½ The sequence can be written 12, 12(½), 12(½)2, 12(½)3, 12(½)4, 12(½)5,.....
Why is multiplying or dividing the numerator and the denominator by the same number the same as multiplying or dividing the fraction by 1?
Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.
