Eureka Math Algebra 1 Module 3 Lesson 3 Problem Set Answer Keyįor Problems 1–4, list the first five terms of each sequence, and identify them as arithmetic or geometric. We know how to find the sum of the first n terms of a geometric series using the formula, Sn a1(1 rn) 1 r. R(n) = 2 n, where n is the number of times we have folded the paper. An infinite geometric series is an infinite sum whose first term is a1 and common ratio is r and is written. We are creating a geometric sequence because each time we fold, we double the number of rectangles. If we fold a rectangular piece of paper in half multiple times and count the number of rectangles created, what type of sequence are we creating? Can you write the formula? For example, think of a sequence of your class schedule, Monday is the first day, Tuesday the second, and so on. This means that, a sequence takes a whole number (say, ' ') and assigns it a real number. is a function from the whole numbers to the real numbers. S(n + 1) = 1.02S(n) for n ≥ 1 for some initial salary S(1). 2.1 Change in Arithmetic and Geometric Sequences. An example of a geometric sequence would be a person’s salary that increases by 2% each year. A recursive formula would be S(n + 1) = S(n) + 2,000 for n ≥ 1 for some initial salary S(1). An example of an arithmetic sequence would be a person’s salary that increases by $2,000 each year. Describe it, and write its formula.Īnswers will vary. Think of a real – world example of an arithmetic or a geometric sequence. But, it is the result that represents reality in this case. This is similar to the linear functions that have the form y mx + b. As shown previously, at -20.08, the geometric mean provides a return thats a lot worse than the 12 arithmetic mean. An arithmetic sequence has a constant difference between each consecutive pair of terms. Engage NY Eureka Math Algebra 1 Module 3 Lesson 3 Answer Key Eureka Math Algebra 1 Module 3 Lesson 3 Exercise Answer Key Two common types of mathematical sequences are arithmetic sequences and geometric sequences.
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