Back to Blog
Algebra 1 geometric sequences7/9/2023 ![]() To define it explicitly, is equal to 100 plus Of- and we could just say a sub n, if we want Is the sequence a sub n, n going from 1 to infinity So this is indeed anĬlear, this is one, and this is one right over here. Is this one arithmetic? Well, we're going from 100. The arithmetic sequence that we have here. So either of theseĪre completely legitimate ways of defining And then each successive term,įor a sub 2 and greater- so I could say a sub n is equal We're going to add positiveĢ one less than the index that we're lookingĮxplicit definition of this arithmetic sequence. So for the secondįrom our base term, we added 2 three times. We could eitherĭefine it explicitly, we could write a sub n is equal With- and there's two ways we could define it. So this is clearly anĪrithmetic sequence. ![]() Then to go from negativeġ to 1, you had to add 2. These are arithmetic sequences? Well let's look at thisįirst one right over here. Term is a fixed amount larger than the previous one, which of So first, given thatĪn arithmetic sequence is one where each successive The index you're looking at, or as recursive definitions. And then just so thatĮither as explicit functions of the term you're looking for, Out which of these sequences are arithmetic sequences. Term is a fixed number larger than the term before it. And if you would like to see more MathSux content, please help support us by following ad subscribing to one of our platforms.Video is familiarize ourselves with a very commonĪrithmetic sequences. 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. ![]()
0 Comments
Read More
Leave a Reply. |