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The geometric sequence with three terms with a sum of nine and the sum to infinity of 8 is -9,-18, and 36. The first term is -9 and the common ratio is -2.

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Q: The sum to three terms of geometric series is 9 and its sum to infinity is 8. What could you deduce about the common ratio. Why. Find the first term and common ratio?
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A geometric series has first term 4 and its sum to infinity is 5 Find the common ratio?


What does summation of infinite series?

The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.

What does Geometric Series represent?

A geometric series represents the partial sums of a geometric sequence. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r)

How can you tell if a infinite geometric series has a sum or not?

The geometric series is, itself, a sum of a geometric progression. The sum of an infinite geometric sequence exists if the common ratio has an absolute value which is less than 1, and not if it is 1 or greater.

How do you find the common ratio in a geometric sequence?

Divide any term in the sequence by the previous term. That is the common ratio of a geometric series. If the series is defined in the form of a recurrence relationship, it is even simpler. For a geometric series with common ratio r, the recurrence relation is Un+1 = r*Un for n = 1, 2, 3, ...

Condition for an infinite geometric series with common ratio to be convergent?

The absolute value of the common ratio is less than 1.

What is a series?

a sequential series of geometric shapes

How do you solve geometric sequence and series?

There can be no solution to geometric sequences and series: only to specific questions about them.

Differentiate between arithmetic series and geometric series?

In an arithmetic series, each term is defined by a fixed value added to the previous term. This fixed value (common difference) may be positive or negative.In a geometric series, each term is defined as a fixed multiple of the previous term. This fixed value (common ratio) may be positive or negative.The common difference or common ratio can, technically, be zero but they result in pointless series.

What is a figural series?

a sequential series of geometric shapes

What is the sum of an infinite geometric series is?

It depends on the series.

Is the series 11 16point5 22 27point5 33 arithmetic geometric or neither?

Arithmetic, common difference 5.5

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