(3) The product of n consecutive integers is always divisible by n! So, 4x5圆 (4*5*6=120) is divisible by 3! (2) The sum of an arithmetic sequence is equal to the mean (average) times the number of terms. (1) The mean and the medium of any arithmetic sequence is equal to the average of the first and last terms. There are some short cuts and concepts that you should know about this topic. (2) Plug in the "n" value into the formula for an arithmetic series. You already know everything you need to after reading this post. This seems to be a popular topic on GMAT forums. Also, notice how my first and last terms are the first term that is a multiple of 7 and the last term that is a multiple of seven within the set! S n = \(\frac\)) + 1Īll you have to do is instead of dividing our old formula by 2, you divide it by the increment. I only put the recursive formula for understanding.įormula for geometric series (when there is a common ratio)įormula for arithmetic series (when there is a common ratio) I only put the recursive formula for understanding.įormula for arithmetic sequence (when there is a common difference)Īgain, you only need to know the explicit formula, because you can find any term with it. In reality, you only need to know the explicit formula, because you can find any term with it. I will then show you how to use the formulas to answer some questions that might not be intuitive of non math geniuses.įormula for geometric sequence (when there is a common ratio) lets give you the formulas that will allow you to answer any question regarding series and sequences. (3) How many integers are there in a sequenceĪnyway, now that you get the point. (1) The sum of numbers in a series (which can be asked in many tricky ways such as the sum of all the numbers, sum of just the even numbers, sum of just the odd numbers, sum of only the numbers which are multiples of 7, sum of the first 10 numbers, and many more tricky ways!) Here are some examples of things you may be asked to find/do with them. There is no limit to what the GMAT can ask you to find when dealing with series and sequences. What the GMAT could ask us to do with sequences and series and how to do it! If you take 'set D' and add the terms, then you have a geometric series. So if you take 'set A' and add the terms then you have an arithmetic series. There you go, now you know the difference. A series is created by adding terms in the sequence. The difference between the two types of sequences is that in arithmetic sequences the consecutive numbers in a set differ by a fixed amount known as the common difference whereas in a geometric sequence the consecutive numbers in a set differ by a fixed number known as the common ratio. In 'set' D' the common ratio is two (32/16=2). Therefore, n 'set F' the common ratio is two. To find the common ratio you simply take the ratio one consecutive number to the one before it. The difference between two consecutive numbers is therefor the common ratio. Therefore, the above sets are geometric sequences. For instance, in 'set F', the first two terms (5 and 10) have a smaller difference than the last two terms (40 and 80). You might notice that the difference between consecutive numbers in the above three sets are not a fixed amount. For example, in 'set C', to find the common difference compute (8-3=5).Ī geometric sequence on the other hand, is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed number called the common ratio. As you most likely noticed already, the common difference is found by finding the difference between two consecutive terms within the sequence. In 'set B' the common difference is the fixed amount of two, and in 'set C' the common difference is the fixed amount of five. In 'set A', the common difference is the fixed amount of one. Geometric sequence vs arithmetic sequenceĪn arithmetic sequence is a sequence of numbers where each new term after the first is formed by adding a fixed amount called the common difference to the previous term in the sequence. They are geometric sequences and arithmetic sequences, and geometric series and arithmetic series. There are two types of sequences and two types of series. The following is meant to help one understand the entire topic that this falls under. I want to make this more clear for people who stumble on this post in the future.
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