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.