#Arithmetic and geometric sequences formulas sum series#
is infinite or in other words, the series doesn’t end anywhere. The third formula is only applicable when the number of terms in the G.P. Therefore, the correct option is D) Geometric Series. Q 1: What type of series is the following sequence of ‘n’ numbers:Īnswer: The above series is clearly a Geometric Progression with the first term = 1 and the common ratio or r = 1 also. The following trick question may be asked from this concept. The second formula works only when r = 1. To find the sum of the first 5 terms, we note that n = 5, a = 3, and r = 2. Also, we see that a = 3, thus we can use the first formula and find the sum of any number of terms of such series. For example, in the above example, 6/3 = 2 and 12/6 = 2. Remember divide two sets of consecutive terms. You can verify it by dividing the consecutive terms. Given that the series is finite: 3, 6, 12, …Īnswer: The first step is to confirm that the series is actually a G.P. For example, consider the following series.Įxample 2: Find the sum of the first 5 terms of the following series. So there are three formulae depending on the value of ‘r’. in case of -1 < r <1 is given by the following formula: can be found out by the following formulae: and ‘r’ be the common ratio, then the sum of the G.P. Here we will list important formulae to find out the sum of the first few terms. For example, the sum of the first ten terms will be denoted by S 10. The sum is denoted by S n where ‘n’ is the number of the term up to which the sum is being found out. Sometimes you will be given the series and asked to find the sum of the first few terms or the entire series. Since the first term is 1, we have to multiply it by 2 9 to get the tenth term = 512. Knowing this the above example becomes very easy. Similarly, we will get the fourth term by multiplying the first term by r 3 and so on. We get the third term by multiplying the first term by ‘r 2‘.
To get the second term, the first term is multiplied by ‘r’. as we saw, each term is multiplied by the common ration ‘r’. Browse more Topics Under Number SeriesĮxample 1: In a G.P., r = 2 and a = 1. In other words, if you know ‘r’ and the first term, you can generate the entire Geometric Progression. Therefore for the series present above, we shall have:Ī 3/a 2 = r where ‘r’ is the common ratio. say a 1, a 2, a 3, …, a n, the ratio of any two consecutive numbers within the series will be same. the ratio of any two consecutive numbers is the same number that we call the constant ratio. This number is called the constant ratio. is formed by multiplying each number or member of a series by the same number. Geometric Series or Geometric Progression
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