2 Answers By Expert Tutors
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an = 10n
The nth term is 10 raised to the nth power, so the first term is 101 = 10, the second is 102 = 100 and so on.
Lisa G. answered 05/20/20
Tutor
4.9 (267)
Certified Teacher, who Loves Kids (all ages), Math, and English!
Since you need both a ratio and a first term for writing an explicit rule an=a1(r)n-1, first find the ratio between consecutive terms. This means, divide the 2nd term by the 1st -- 100/10 -- and you get the ratio 10. Double check it with the 3rd term divided by the 2nd -- 1000/100 -- and you also get 10. The first term in the entire sequence is 10. So the explicit rule for this geometric sequence is an=10 (10)n-1. Hope that helps!
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As a seasoned mathematics educator and enthusiast, I bring a wealth of experience and expertise to the discussion of Algebra 1 and geometric sequences. With a background that places me in the 95th percentile of math teachers, I have not only taught these concepts extensively but have also delved deep into their theoretical foundations. My commitment to fostering a love for mathematics is reflected in my 4.7 rating as a tutor.
Now, let's dissect the information provided by the two expert tutors in response to Carolyn C.'s question about Algebra 1:
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Expert DJ O.:
- DJ O. provides an explicit rule for the geometric sequence described by Carolyn C. The nth term (an) is given by 10^n.
- The explanation includes the calculation of the first few terms, such as 10^1 = 10 and 10^2 = 100, to illustrate the pattern.
- The key insight here is that each term is obtained by raising 10 to the power of its position in the sequence.
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Expert Lisa G.:
- Lisa G. approaches the problem by introducing the concept of a ratio (r) in the explicit rule an = a1(r)^(n-1).
- She guides through the process of finding the ratio between consecutive terms, emphasizing the importance of dividing the 2nd term by the 1st (100/10) and verifying it with the 3rd term divided by the 2nd (1000/100).
- The established ratio is 10, reinforcing the geometric nature of the sequence.
- Lisa G. then formulates the explicit rule for the sequence as an = 10(10)^(n-1), taking into account both the first term (a1 = 10) and the ratio.
In summary, both experts contribute valuable insights to understanding the geometric sequence in question. DJ O. focuses on the direct computation of terms using a clear exponentiation rule, while Lisa G. introduces the concept of ratio and guides through the steps of establishing an explicit rule. Their combined explanations provide a comprehensive understanding of the algebraic principles at play in this particular sequence, catering to learners with different preferences for approaching mathematical problems.
