Don’t worry, we’ve prepared more problems for you to work on as well Example 1 Find the sum of the series, 3 6. ![]() 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. S a 1 r 81 1 1 3 243 2 These two examples clearly show how we can apply the two formulas to simplify the sum of infinite and finite geometric series. To make work much easier, sequence formula can be used to find out the last. That is each subsequent number is increasing by 3. To recall, all sequences are an ordered list of numbers. You are paid $15\%$ interest on your deposit at the end of each year (per annum). Sequence formula mainly refers to either geometric sequence formula or arithmetic sequence formula. 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. ![]() Example Show that the sequence 3, 6, 12, 24, is a geometric sequence, and find the next three terms. ![]() If the dots have nothing after them, the sequence is infinite. In a (geometric) sequence, the term to term rule is to multiply or divide by the same value. If the dots are followed by a final number, the sequence is finite. geometric sequence: An ordered list of numbers in which each term after the first is found by multiplying the previous one by a fixed non-zero number called the. Note: The 'three dots' notation stands in for missing terms. We can therefore determine whether a sequence is arithmetic or geometric by working out whether adjacent terms differ by a common difference, or a common ratio. is a finite sequence whose end value is $19$.Īn infinite sequence is a sequence in which the terms go on forever, for example $2, 5, 8, \dotso$. For example, $1, 3, 5, 7, 9$ is a sequence of odd numbers.Ī finite sequence is a sequence which ends. 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.
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