![]() ![]() If the rule is to add or subtract a number each time, it is called an arithmetic sequence. Continuing, the third term is: a3 ( a + d) + d. ![]() Since we get the next term by adding the common difference, the value of a2 is just: a2 a + d. For arithmetic sequences, the common difference is d, and the first term a1 is often referred to simply as 'a'. Of course, we want it to give either $0$ or $1$, and the way to create a $0$ a $1+(-1)$, but apart from that, this is just one of those things you have to play with to understand and remember. 1 2 3 4 5 6 Sequences Number sequences are sets of numbers that follow a pattern or a rule. Since arithmetic and geometric sequences are so nice and regular, they have formulas. if $n$ of $a_n$ was odd).Įdit: here's a perfectly legitimate formula. An arithmetic sequence can be defined by an explicit formula in which an d (n - 1) + c, where d is the common difference between consecutive terms, and c a1. $n$ of $a_n$ was even), or plus $1$ if the previous term was odd (i.e. Arithmetic Sequence Arithmetic Progression Explicit Formula: an a1 + (n 1)d Example 1: 3, 7, 11, 15, 19 has a1 3, d 4, and n 5. Sequences are a special type of function that are useful for describing patterns. 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. ![]() If the initial term ( a0) of the sequence is a and the common difference is d, then we have, Recursive definition: an an 1 + d with a0 a. Hint: each term $a_n$ equals the previous term, plus $0$ if the previous term was even (i.e. WolframAlpha has faculties for working with and learning about commonly occurring sequences like the Fibonacci sequence, the Lucas sequence, arithmetic. Arithmetic Sequences If the terms of a sequence differ by a constant, we say the sequence is arithmetic. ![]()
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