The 16th term of a sequence 7, 10, 13, 16… is ________:
A. 55
B. 58
C. 61
D. 64
Explanation:
The given sequence has a common difference of 3. We can use the formula for the nth term of an arithmetic sequence to find the 16th term:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Substituting the given values, we get:
a16 = 7 + (16-1)3
a16 = 7 + 45
a16 = 52
Therefore, the 16th term of the sequence is 52.
Understanding Arithmetic Sequences: Definition and Examples
Arithmetic sequences are an important topic in mathematics and are used in a variety of real-life applications. In this article, we will define what an arithmetic sequence is and provide some examples to help you better understand this concept.
An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed number, called the common difference, to the previous term. For example, the sequence 2, 5, 8, 11, 14, 17 is an arithmetic sequence with a common difference of 3.
To find the nth term of an arithmetic sequence, we use the formula:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, d is the common difference, and n is the term number we want to find.
Let’s take an example to understand this formula better. Consider the sequence 4, 7, 10, 13, 16, 19. We can find the 10th term of this sequence using the formula:
a10 = 4 + (10-1)3
a10 = 4 + 27
a10 = 31
Therefore, the 10th term of the sequence is 31.
Arithmetic sequences are used in a variety of real-life situations. For example, if a company produces 100 units of a product in the first month, 150 units in the second month, and 200 units in the third month, we can say that the company is using an arithmetic sequence to increase production each month. Similarly, if an investor deposits a fixed amount of money each year and earns a fixed rate of interest, the total amount of money in the account will follow an arithmetic sequence.
In conclusion, arithmetic 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 finance, engineering, and science.
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General Knowledge MCQs by CSSMCQS
General Knowledge MCQs by CSSMCQS
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Conclusion
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