You are paid $15\%$ interest on your deposit at the end of each year (per annum). The general form of the geometric sequence formula is: ana1r(n1), where r is the common ratio, a1 is the first term, and n is the placement of the term. We refer to $£A$ as the principal balance.
#Formulas for sums of geometric and arithmetic sequences plus
Simple and Compound Interest Simple Interest The first term in the series is a, and the last one is a+(n-1)d, so we can say the sum of the series is the first term plus the last term multiplied by the. 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. If the dots are followed by a final number, the sequence is finite. Note: The 'three dots' notation stands in for missing terms. It is found by using one of the following formulas: S n a 1 a 1 r n 1 r o r S n a 1 ( 1 r n) 1 r Video lesson Use the formula for the sum of a geometric series to determine the sum when a 1 4 and r2 and we have 12 terms. is a finite sequence whose end value is $19$.Īn infinite sequence is a sequence in which the terms go on forever, for example $2, 5, 8, \dotso$. Just as with arithmetic series it is possible to find the sum of a geometric series. We quickly recognize that the terms have a common difference of 5, and this is therefore the sum of an arithmetic sequence whose explicit formula is an5n+3. 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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