Math Tutoring on Sequences
A sequence is an ordered list of terms or elements. For example a1, a2, a3, ..… aₓ. Each term in a sequence is identified by its location in the sequence. So a1 is the first term in the sequence, a2 would be the second term; a3 would be the third term and so on. There are two types of sequences, a finite sequence, and an infinite sequence. A finite sequence is a sequence that has a specific number of terms and an infinite sequence is the one which continues on forever. So the value of n is based upon the term that we are looking for in the sequence. Another way to express a sequence is a recursive formula, and this means that each term in a sequence is based upon previous terms not the value of n. Now let’s talk about two different types of sequences, one is an arithmetic sequence and the other is a geometric sequence. An arithmetic sequence is a sequence that has the pattern of adding the same value to determine consecutive terms and we say arithmetic sequences have a common difference. To find the common difference, we can pick any term and subtract the term before it. For a geometric sequence, the pattern is that we multiply by a constant to determine consecutive terms. We see geometric sequences have a common ratio other than a common difference. We can calculate that by taking any term in the sequence and dividing by the term before it.
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1. What is an Arithmetic sequence?
2. Define Geometric sequence.
3. What is the Recursive formula?
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