Question: In An Infinite Geometry Series, If R Is Above 1, Then What?

If |r| > 1, the terms of the series become larger and larger in magnitude. The sum of the terms also gets larger and larger, and the series does not converge to a sum. (The series diverges.)

What if r is greater than 1 in infinite geometric series?

But in the case of an infinite geometric series when the common ratio is greater than one, the terms in the sequence will get larger and larger and if you add the larger numbers, you won’t get a final answer.

What happens if r1?

If r is equal to 1, all of the terms of the series are the same. The series diverges. If r is −1, the terms take two values alternately (e.g.,2,−2,2,−2,2,−2,⋯) ( e.g., 2, − 2, 2, − 2, 2, − 2, ⋯ ). The sum of the terms oscillates between two values (e.g.,2,0,2,0,2,0,⋯) ( e.g., 2, 0, 2, 0, 2, 0, ⋯ ).

What is r in infinite geometric series?

Since this ratio is common to all consecutive pairs of terms, it is called the common ratio. It is denoted by r. If the ratio between consecutive terms is not constant, then the sequence is not geometric. The formula for the common ratio of a geometric sequence is r = an+1 / an.

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What does r represent in geometric series?

Recall that a geometric sequence is a sequence in which the ratio of any two consecutive terms is the common ratio, r.

What is the formula in finding the sum of infinite geometric sequence if r 1?

To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.

What are the value of a1 and r of the geometric series?

Answer: The values of a1 and r are 2 and -1 respectively.

What is r in GP?

In a G.P. the ratio of any two consecutive numbers is the same number that we call the constant ratio. It is usually denoted by the letter ‘r’. a 3/a2 = r; where ‘r’ is the common ratio.

How do you find the common ratio r and nth term of a geometric sequence?

6. How do you find the nth term of a geometric progression with two terms? First, calculate the common ratio r by dividing the second term by the first term. Then use the first term a and the common ratio r to calculate the nth term by using the formula an=arn−1 a n = a r n − 1.

What is the sum of infinite AP?

The sum to infinity for an arithmetic series is undefined.

What is the r in a geometric sequence?

The number multiplied (or divided) at each stage of a geometric sequence is called the “common ratio” r, because if you divide (that is, if you find the ratio of) successive terms, you’ll always get this common value.

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How is r in GP calculated?

Geometric Progression The nth term of a GP series is Tn = arn1, where a = first term and r = common ratio = Tn/Tn1). The sum of infinite terms of a GP series S= a/( 1-r ) where 0< r<1. If a is the first term, r is the common ratio of a finite G.P. consisting of m terms, then the nth term from the end will be = arm-n.

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