5 4 3 2 1 formula Start with the regular formula 1 2 3 n n n 1 2 and subtract off the part you don t want 1 2 3 4 4 4 1 2 10 Sum for 5 6 7 8 n n n 1 2 10
Solution Arithmetic sequences The common difference equals 1 The sum of the sequence equals 15 The explicit formula of this sequence is a n 5 n 1 1 The recursive formula of this sequence is a n a n 1 1 The nth terms 5 4 3 2 1 0 1 2 See steps Other Ways to Solve Arithmetic sequences This can be written as 5 cdot 5 5 cdot 4 cdot 4 5 cdot 4 cdot 3 cdot3 5 cdot 4 cdot 3 cdot 2 cdot 2 5 cdot 1 frac 5 4 cdot 5 frac 5 3 cdot 4 frac 5 2 cdot 3 frac 5 1 cdot 2 frac 5 0 cdot 1 Then the general formula is
5 4 3 2 1 formula
5 4 3 2 1 formula
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5 4 3 2 1
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The partial sums of the series 1 2 3 4 5 6 are 1 3 6 10 15 etc The n th partial sum is given by a simple formula k 1 n k n n 1 2 displaystyle sum k 1 n k frac n n 1 2 This arithmetic sequence calculator also called the arithmetic series calculator is a handy tool for analyzing a sequence of numbers that is created by adding a constant value each time You can use it to find any property of the sequence the first term common difference n term or the sum of the first n terms
This formula allows us to simply plug in the number of the term we are interested in and we will get the value of that term In order to find the fifth term for example we need to plug n 5 into the explicit formula a 5 3 2 5 1 3 2 4 3 8 11 Cool Place the four arithmetic signs plus minus times and divided by between the digits and as many parentheses as you like around the digits How many numbers from 1 to 40 can you get In the same style as my Yearly Number Challenge Posters I made a set of 5 4 3 2 1 Challenge Posters
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Rule xn xn 1 xn 2 Now what does xn 1 mean It means the previous term as term number n 1 is 1 less than term number n And xn 2 means the term before that one Let s try that Rule for the 6th term x 6 x 6 1 x 6 2 x 6 x 5 x 4 So term 6 equals term 5 plus term 4 We already know term 5 is 21 and term 4 is 13 so x 6 21 13 34 The Rule for any term is xn 10 3 n 1 So the 4th term is x 4 10 3 4 1 10 3 3 10 27 270 And the 10th term is x 10 10 3 10 1 10 3 9 10 19683 196830 A Geometric Sequence can also have smaller and smaller values Example 4
The mathematical formaula is given below Therefore according to this formula we have 5 5 1 2 5 6 2 5 3 15 Therefore the sum of the series is 15 Continue Reading More answers below Rohit Bhati BTech in Computer Science Engineering Birla Institute of Technology Jaipur Graduated 2022 5 y 5 4 3 2 1 15 4 5 By creating little diagrams like this I ve figured out the pattern which is as follows Users Comparisons 2 1 3 3 2 4 6 3 5 10 4 6 15 5 7 21 6 8 28 7 9 36 8
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5 4 3 2 1 formula - This arithmetic sequence calculator also called the arithmetic series calculator is a handy tool for analyzing a sequence of numbers that is created by adding a constant value each time You can use it to find any property of the sequence the first term common difference n term or the sum of the first n terms