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paulbdiggs
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If given the values -1, 5, 2 in this sequence, what would be the missing term to make this a geometric series?
Also, what would the sum of this geometric series be?
Also, what would the sum of this geometric series be?
What geometric series are you talking about? If you mean that a sequence starts -1, 5, 2, ... , that is NOT a geometric sequence: a geometric sequence is either always increasing (if the constant ratio is larger than 1) or decreasing (if it is less than 1).paulbdiggs said:If given the values -1, 5, 2 in this sequence, what would be the missing term to make this a geometric series?
Also, what would the sum of this geometric series be?
A geometric series is a series of numbers where each term is multiplied by a constant ratio to get the next term. For example, 2, 4, 8, 16, 32 is a geometric series with a common ratio of 2.
The sum of a geometric series can be calculated using the formula S = a * (1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms. Alternatively, you can also use the formula S = (a * (1 - r^n)) / (1 - r) - a, where a is the first term, r is the common ratio, and n is the number of terms minus 1.
The common ratio in a geometric series is the constant number that is multiplied by each term to get the next term. It is often denoted by the letter r.
Yes, the sum of a geometric series can be infinite if the common ratio is greater than 1. In this case, the series will continue to grow without ever reaching a finite sum.
A finite geometric series has a limited number of terms and therefore, a finite sum. An infinite geometric series, on the other hand, has an unlimited number of terms and may or may not have a finite sum depending on the value of the common ratio.