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)
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)
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 10.
· Geometric Sequence (geometric progression) - a sequence of numbers in which each term is obtained by multiplying the preceding term by the same number (common ratio). The following is a geometric progression: 1, 2, 4, 8, 16, 32… The common ratio for this geometric progression is 2.
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.
Yes, that's what a geometric sequence is about.
If I understand your question, you are asking what kind of sequence is one where each term is the previous term times a constant. The answer is, a geometric sequence.
The inverse of multiplying is dividing, so dividing by 2.
a sequence of shifted geometric numbers
The inverse operation of Multiplying is Dividing.
Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.
Details about multiplying and dividing rational number involves modeling multiplying fractions by dividing squares to equal segments and then overlap the squares.