![]() ![]() At the end of the first year you will have a total of: \ With simple interest, the key assumption is that you withdraw the interest from the bank as soon as it is paid and deposit it into a separate bank account. You are paid $15\%$ interest on your deposit at the end of each year (per annum). We refer to $£A$ as the principal balance. ![]() Simple and Compound Interest Simple Interest For example, \ so the sequence is neither arithmetic nor geometric. A series does not have to be the sum of all the terms in a sequence. The starting index is written underneath and the final index above, and the sequence to be summed is written on the right. We call the sum of the terms in a sequence a series. The Summation Operator, $\sum$, is used to denote the sum of a sequence. If the dots have nothing after them, the sequence is infinite. What is an arithmetic Sequence An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed number to the previous term. ![]() If the dots are followed by a final number, the sequence is finite. The formula for the nth term of an arithmetic sequence is an a1 (n-1)d, where a1 is the first term of the sequence, an is the nth term of the sequence, and d is the common difference. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 14 16). Note: The 'three dots' notation stands in for missing terms. Computation of the sum 2 5 8 11 14. is a finite sequence whose end value is $19$.Īn infinite sequence is a sequence in which the terms go on forever, for example $2, 5, 8, \dotso$. An arithmetic sequence is a sequence of numbers which increases or decreases by a constant amount each term. For example, $1, 3, 5, 7, 9$ is a sequence of odd numbers.Ī finite sequence is a sequence which ends. Let me know, if someone has found something wrong with this.Contents Toggle Main Menu 1 Sequences 2 The Summation Operator 3 Rules of the Summation Operator 3.1 Constant Rule 3.2 Constant Multiple Rule 3.3 The Sum of Sequences Rule 3.4 Worked Examples 4 Arithmetic sequence 4.1 Worked Examples 5 Geometric Sequence 6 A Special Case of the Geometric Progression 6.1 Worked Examples 7 Arithmetic or Geometric? 7.1 Arithmetic? 7.2 Geometric? 8 Simple and Compound Interest 8.1 Simple Interest 8.2 Compound Interest 8.3 Worked Examples 9 Video Examples 10 Test Yourself 11 External Resources SequencesĪ sequence is a list of numbers which are written in a particular order. Arithmetic Series Fit two trapezoids together, then divide by 2 Historical note Reversing the sequence Write the process as a formula A little more algebra. Recently I was trying to figure out how to find the nth term in a series, or sequence, where the differences ($d$) between the elements of the series are not constant, but if $d$ for each $A_n - A_ 7 = 28$$Ģ) There are other methods exist to find $A_n$ in these type of sequences, may be they are easier, I don't know.ģ) I am not sure if I am the first person to derive this formula, if I am not, then I apologize. ![]() So, may be it's stupid, but I am posting my formula here in Stack Exchange. I don't know what to do to tell the world about whatever I found. So please forgive me if my writing is not so impressive! First of all, I am a 12th grader so I don't know how to write research notes. Formula List Questions and Solutions Problems to Solve FAQs What is Arithmetic Progression In mathematics, there are three different types of progressions. ![]()
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