14. If you were to shade in a nxn square on graph paper, you could do it the boring way (with sides parallel to the edge of the paper) or the interesting way, as illustrated below: The interesting thing here, is that a 3 x 3 square now has area 13. Our goal is the find a formula for the area of a n x n (diagonal) square. a. Write out the first few terms of the sequence of areas (assume a1 = 1, a2 = 5, etc). Is the sequence arithmetic or geometric? If not, is it the sequence of partial sums of an arithmetic or geometric sequence? Explain why your answer is correct, referring to the diagonal squares. b. Use your results from part (a) to find a closed formula for the sequence. Show your work. Note, while there are lots of ways to find a closed formula here, you should use partial sums specifically. C. Find the closed formula in as many other interesting ways as you can.

14. If you were to shade in a nxn square on graph paper, you could do it the boring way (with sides parallel to the edge of the paper) or the interesting way, as illustrated below: The interesting thing here, is that a 3 x 3 square now has area 13. Our goal is the find a formula for the area of a n x n (diagonal) square. a. Write out the first few terms of the sequence of areas (assume a1 = 1, a2 = 5, etc). Is the sequence arithmetic or geometric? If not, is it the sequence of partial sums of an arithmetic or geometric sequence? Explain why your answer is correct, referring to the diagonal squares. b. Use your results from part (a) to find a closed formula for the sequence. Show your work. Note, while there are lots of ways to find a closed formula here, you should use partial sums specifically. C. Find the closed formula in as many other interesting ways as you can.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.2: Sequences, Series And Summation Notation

Problem 40E: Find the sum of the first five terms of the sequence with the given general term. an=2n+1

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