The fact that a geometric sequence has a common factor allows you to do two things. The first is to calculate any random element in the sequence (which mathematicians like to call the "nth" element), and the second is to find the sum of the geometric sequence up to the n...
Summing a Geometric Sequence Sometimes, we want to find the sum of the first however many terms of a geometric sequence. If there aren't many terms to count, this is nice and easy. However, if you want to quickly add the first 50 terms, for example, adding them manually would take a...
Calculate the first term in the sequence using the formula a = t/[f^(n - 1)], in cases where you are given a single number, t, and its position in the sequence, n, as well as the factor. So if the second term in the sequence (at n = 2) is 6 and f = 2, a = 6/[2...
If a is the first term and r is the constant ratio of a geometric sequence, then the geometric sequence can be written as a, ar, ar2, ar3,……. ar n– 1 or a, ar, ar2, ar3, ar4,…….. ar n– 1,….. according to as it is finite or infinite....
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To determine whether a sequence is arithmetic, geometric, or neither we test the terms of the sequence. We test for a common difference or a common ratio. If neither test is true, then we have a sequence that is neither geometric nor arithmetic. ...
Enter the first two terms of your geometric sequence below as a decimal to calculate the sum to infinity of the series. Enter the 1st Term* Enter the 2nd Term* The sum to infinity is: Negative Sum to Infinity The sum to infinity of a geometric series will be negative if the first term...
A geometric growth rate means all consecutive terms in the sequence have the same ratio to one another, equivalent to growing at a constant rate or percentage. Knowing how to calculate this sort of thing is very useful when looking at real-world applicat
Calculate the missing terms of the geometric sequence ...,2, ?,?,?, 512,... Find the sum of the first four terms of the geometric sequence with a= -3 and r= 3. Find the sum of the first 12 terms of the geometric sequence: 3, 6, 12, 24, ... Find the sum of the first ...
It was not perfectly clear to me what you needed to leave as a variable, and what is a constant. But, this should get you started.