The geometry series chapter and examples of geometric series problems

Definition of Geometry Series

The definition of Geometry sequence is a sequence where each tribe is obtained from the product of the previous tribe with a constant. Geometry series are sequences that fulfill the quotient of a term with consecutive terms that have a constant value.

Example :
the geometric sequence is a,b, and c then c / b = b / a = constant. The quotient of an adjacent term is called a ratio (r).

For example found a geometrical series as below

U1, U2, U3 ,… ,A 1, A
Then U2 / U1, U3 / U2,…, Un / Un-1 = r
How to determine the nth quarter of a geometry line?
Check out the explanation below

U3 / U2 = r so, U3 = U2.r = a.r.r = ar2
Un / Un-1 = r jadi, One = One-1. r = arn-2.r = arn-2+1 = arn-1
Then it can be concluded that the geometric formula for the nth term geometry line is Un = arn-1

a= initial rate r ratio.

Geometry Series Formulas

The first number n of the geometric sequence is called the geometric sequence. Suppose the fourth quarter of the geometry line is formulated an = a1rn – 1, then the geometry series can be written as,

Sn = a1 + a1r + a1r2 + a1r3 … + a1r-1

If we multiply the series by –r then adds them by the original series, then it will get

Until then Sn – rSn = a1 – a1rn. By solving the equation for Sn, then get

The above result is the formula for the sum of the first n terms of an infinite geometric sequence.

Number n First Quarter Geometry

Given the geometry line with the first quarter a1 and the ratio r, the number of n first terms i.e.

can be said: The sum of the geometric lines is equal to the difference of the first term and the term n + 1, then divided by 1 minus the ratio.

Examples of Geometry Series Questions

Question: Count the amount 9 first quarter of the line an = 3n.

Answer:

total 9 the first term can be denoted in the sigma notation below

From the series obtained the first term a1 = 3, rasio r = 3, and the number of terms n = 9. By using the formula for the number of n first terms

Then, the first nine quarters of the line an = 3n that is 29.523.

Such is the language of geometry series, May be useful

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