Arithmetic sequence equation1/30/2024 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). Use this formula to calculate the sum of the first 100 terms of the sequence defined by an 2n 1. We refer to $£A$ as the principal balance. 2Sn n(a1 + an) Dividing both sides by 2 leads us the formula for the n th partial sum of an arithmetic sequence17: Sn n(a1 + an) 2. 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. Sn n/2(2a+(n-1)d) Suppose we have an AP with first term a and common difference d, then we can write the sum of the first n terms as: Sn a + (a+d) +. 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 recursive equation for an arithmetic squence is: f (1) the value for the 1st term. The Summation Operator, $\sum$, is used to denote the sum of a sequence. If you want the 2nd term, then n2 for 3rd term n3 etc. 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. 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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