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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 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)

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, ...

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

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

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1/8

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.

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)

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.

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, ...

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

a sequential series of geometric shapes

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

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.

a sequential series of geometric shapes

It depends on the series.

Arithmetic, common difference 5.5

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