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...
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 long time. We want a sho...
In mathematics, a geometric sequence is a sequence in which the ratio comparing each term in the sequence to the term that came before it in the sequence is constant. We call that ratio the common ratio of a geometric sequence, and we represent the nth term of the sequence with the notat...
A sequence of non-zero numbers is called a geometric sequence, also known as geometric progression (G. P ) if the ratio of a term and the term preceding it is always a constant quantity.The constant ratio is called the common ratio of the geometric sequence....
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...
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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.
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Example Problem 1: Arithmetic or Geometric Is the sequence {eq}{1,1,2,3,5,8,13,21,\dots } {/eq} arithmetic, geometric, or neither? Step 1: See if there is a common difference. Subtract the first term from the second term, and you get zero. ...
Enter the first two terms of a geometric sequence into the calculator below to calculate its sum to infinity. Sum to Infinity CalculatorEnter 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...