![]() ![]() In the above equation, b n is the nth term of the sequence that we wish to calculate, b 1 is the first term of the sequence, r is the common difference or ratio between the terms, and n is the nth term of the sequence. Formula of the geometric sequenceįor geometric sequence, we use an equation to calculate the n th term of the sequence having a constant difference. The sequence is usually represented by the series but a little bit different in that the sequence is separated by commas while in series sum notation is used instead of commas.Ī sequence is usually of the form like 1, 4, 16, 64, 256, 1024,… in this sequence all the terms are multiplied by themselves by 4 for making a common difference. What is a Geometric sequence?Ī geometric sequence usually states that a series of numbers comes by taking a common difference or by multiplying each term by a constant. In this post, we will learn about the sequence, geometric sequence, and how to calculate it, with a lot of examples. The terms are used to create a common difference by multiplying the previous digit. A sequence is generally the set of numbers having equal differences among the numbers and are separated by commas. And if you would like to see more MathSux content, please help support us by following ad subscribing to one of our platforms.A geometric sequence is a type of sequence. Still, got questions? No problem! Don’t hesitate to comment below or reach out via email. ![]() Personally, I recommend looking at the finite geometric sequence or infinite geometric series posts next! Looking to learn more about sequences? You’ve come to the right place! Check out these sequence resources and posts below. Other examples of explicit formulas can be found within the arithmetic sequence formula and the harmonic series. We were able to do this by using the explicit geometric sequence formula, and most importantly, we were able to do this without finding the first 14 previous terms one by one…life is so much easier when there is an explicit geometric sequence formula in your life! For example, in the first example we did in this post (example #1), we wanted to find the value of the 15th term of the sequence. A great way to remember this is by thinking of the term we are trying to find as the nth term, which is unknown.ĭid you know that the geometric sequence formula can be considered an explicit formula? An explicit formula means that even though we do not know the other terms of a sequence, we can still find the unknown value of any term within the given sequence. N= Another interesting piece of our formula is the letter n, this always stands for the term number we are trying to find. The common ratio is the number that is multiplied or divided to each consecutive term within the sequence. ![]() R= One key thing to notice about the formula below that is unique to geometric sequences is something called the Common Ratio. In this case, our sequence is 4,8,16,32, …… so our first term is the number 4. Take a look at the geometric sequence formula below, where each piece of our formula is identified with a purpose.Ī 1 = The first term is always going to be that initial term that starts our geometric sequence. In this geometric sequence, it is easy for us to see what the next term is, but what if we wanted to know the 15 th term? Instead of writing out and multiplying our terms 15 times, we can use a shortcut, and that’s where the Geometric Sequence formula comes in handy! Geometric Sequence Formula: If the pattern were to continue, the next term of the sequence above would be 64. Notice we are multiplying 2 by each term in the sequence above. ![]()
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