Find the 8th term of the sequence whose general term is 2n2
A. 64
B. 128
C. 256
D. 512
Explanation:
The general term of the given sequence is 2n2. To find the 8th term, we can substitute n=8 into the formula:
an = 2n2
a8 = 2(8)2
a8 = 2(64)
a8 = 128
Therefore, the 8th term of the sequence is 128.
Understanding Sequences in Mathematics: Definition and Examples
In mathematics, a sequence is a list of numbers arranged in a particular order. Sequences can be finite or infinite and can be defined in a variety of ways. In this article, we will define what a sequence is and provide some examples to help you better understand this concept.
A sequence is a function whose domain is the set of positive integers. Each element of the sequence is called a term, and the position of a term in the sequence is called its index. For example, the sequence 1, 2, 3, 4, 5, … is an infinite sequence with first term 1, second term 2, and so on.
Sequences can be defined using explicit formulas, recursive formulas, or by listing the terms. An explicit formula gives a direct formula for finding any term of the sequence, while a recursive formula defines each term in terms of the previous term(s).
Let’s take an example to understand this better. Consider the sequence 3, 7, 11, 15, 19, … . We can define this sequence using an explicit formula:
an = 4n – 1
where n is the index of the term. For example, the 8th term of this sequence can be found by substituting n=8 into the formula:
a8 = 4(8) – 1
a8 = 31
Therefore, the 8th term of the sequence is 31.
Sequences are used in a variety of real-life situations, including in computer science, physics, and finance. For example, in finance, the future value of an investment can be calculated using a sequence formula. Similarly, in physics, the position of an object over time can be represented as a sequence.
In conclusion, sequences are an important concept in mathematics and have many real-life applications. Understanding this concept is essential for solving problems in a variety of fields, including science, finance, and engineering.
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