Explanation Given information: The sequences for which graph is to be drawn are as below, 43. 18 + 6 + 2 + ⋯ 44. 80 + 20 + 5 + ⋯ 45. 7 + 3 + 9 7 + ⋯ 46. 12 + 9 + 27 4 + ⋯ And 47. 3 + 15 + 75 + ⋯ 48. 2 + 3 + 9 2 + ⋯ 49. 4 − 6 + 9 − 27 2 + ⋯ 50. − 6 + 3 − 3 2 + 3 4 + ⋯ And 51. 0.43 + 0.0043 + 0.000043 + ⋯ 52. 0.37 + 0.0037 + 0.000037 + ⋯ 53. $ 500 ( 1.02 ) − 1 + $ 500 ( 1.02 ) − 2 + $ 500 ( 1.02 ) − 3 + ⋯ 54. $ 1000 ( 1.08 ) − 1 + $ 1000 ( 1.08 ) − 2 + $ 1000 ( 1.08 ) − 3 + ⋯ Consider the first geometric sequence. 18 + 6 + 2 + ⋯ Follow these steps in order to calculate draw the graph using the above table considering n at horizontal axis and a n on vertical axis. Step 1: Click on ON button. Step 2: Click on WINDOW and set the following values. Xmin = 0.8 Xmax = 3.2 Xscl = 1 Ymin = − 0.72 Ymax = 20.72 Yscl = 1 Xres = 1 Step 3: Click 2nd and the click Y= . Step 4: Click 1 , select scatter graph and select On. Step 5: Click STAT and select Edit. Step 6: Substitute values 1 , 2 , 3 in column L 1 and enter the values 18 , 6 , 2 in column L 2 . Step 7: Click ZOOM and select ZoomStat The graph obtained following the above steps is given below. The graph shows that as the value of n increases the graph approaches the horizontal line. It can be inferred that there is a limit for the sequence 18 + 6 + 2 + ⋯ . Consider the second geometric sequence. 80 + 20 + 5 + ⋯ Follow these steps in order draw the graph using the above table considering n at horizontal axis and a n on vertical axis. Step 1: Click on ON button. Step 2: Click on WINDOW and set the following values. Xmin = 0.8 Xmax = 3.2 Xscl = 1 Ymin = − 7.75 Ymax = 92.75 Yscl = 1 Xres = 1 Step 3: Click 2nd and the click Y= . Step 4: Click 1 , select scatter graph and select On. Step 5: Click STAT and select Edit. Step 6: Substitute values 1 , 2 , 3 in column L 1 and enter the values 80 , 20 , 5 in column L 2 . Step 7: Click ZOOM and select ZoomStat The graph obtained following the above steps is given below. The graph shows that as the value of n increases the graph approaches the horizontal line. It can be inferred that there is a limit for the sequence 80 + 20 + 5 + ⋯ . Consider the third geometric sequence. 7 + 3 + 9 7 + ⋯ Follow these steps in order draw the graph using the above table considering n at horizontal axis and a n on vertical axis. Step 1: Click on ON button. Step 2: Click on WINDOW and set the following values. Xmin = 0.8 Xmax = 3.2 Xscl = 1 Ymin = 0.314 Ymax = 7.9714 Yscl = 1 Xres = 1 Step 3: Click 2nd and the click Y= . Step 4: Click 1 , select scatter graph and select On. Step 5: Click STAT and select Edit. Step 6: Substitute values 1 , 2 , 3 in column L 1 and enter the values 7 , 3 , 9 7 in column L 2 . Step 7: Click ZOOM and select ZoomStat The graph obtained following the above steps is given below. The graph shows that as the value of n increases the graph approaches the horizontal line. It can be inferred that there is a limit for the sequence 7 + 3 + 9 7 + ⋯ . Consider the fourth geometric sequence. 12 + 9 + 27 4 + ⋯ Follow these steps in order draw the graph using the above table considering n at horizontal axis and a n on vertical axis. Step 1: Click on ON button. Step 2: Click on WINDOW and set the following values. Xmin = 0.8 Xmax = 3.2 Xscl = 1 Ymin = 5.8575 Ymax = 12.8925 Yscl = 1 Xres = 1 Step 3: Click 2nd and the click Y= . Step 4: Click 1 , select scatter graph and select On. Step 5: Click STAT and select Edit. Step 6: Substitute values 1 , 2 , 3 in column L 1 and enter the values 12 , 9 , 27 4 in column L 2 . Step 7: Click ZOOM and select ZoomStat The graph obtained following the above steps is given below. The graph shows that as the value of n increases the graph approaches the horizontal line. It can be inferred that there is a limit for the sequence 12 + 9 + 27 4 + ⋯ . Consider the fifth geometric sequence. 3 + 15 + 75 + ⋯ Follow these steps in order draw the graph using the above table considering n at horizontal axis and a n on vertical axis. Step 1: Click on ON button. Step 2: Click on WINDOW and set the following values. Xmin = 0.8 Xmax = 3.2 Xscl = 1 Ymin = − 9.24 Y max = 87.24 Yscl = 1 Xres = 1 Step 3: Click 2nd and the click Y= . Step 4: Click 1 , select scatter graph and select On. Step 5: Click STAT and select Edit. Step 6: Substitute values 1 , 2 , 3 in column L 1 and enter the values 3 , 15 , 75 in column L 2 . Step 7: Click ZOOM and select ZoomStat The graph obtained following the above steps is given below. The graph shows that as the value of n increases the graph does not approaches the horizontal line. It can be inferred that there is a no limit for the sequence 3 + 15 + 75 + ⋯ . Consider the Sixth geometric sequence. 2 + 3 + 9 2 + ⋯ Follow these steps in order draw the graph using the above table considering n at horizontal axis and a n on vertical axis. Step 1: Click on ON button. Step 2: Click on WINDOW and set the following values. Xmin = 0.8 Xmax = 3.2 Xscl = 1 Ymin = 1.575 Y max = 4.925 Yscl = 1 Xres = 1 Step 3: Click 2nd and the click Y= . Step 4: Click 1 , select scatter graph and select On. Step 5: Click STAT and select Edit. Step 6: Substitute values 1 , 2 , 3 in column L 1 and enter the values 2 , 3 , 9 2 in column L 2 . Step 7: Click ZOOM and select ZoomStat The graph obtained following the above steps is given below. The graph shows that as the value of n increases the graph does not approaches the horizontal line. It can be inferred that there is a no limit for the sequence 2 + 3 + 9 2 + ⋯

7th Edition

ISBN: 9780134494807

Author: BITTINGER

Publisher: PEARSON CO

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 14.3, Problem 87ES

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How the graph of geometric sequence can be used in order to determine whether the sequence has a limit.

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Chapter 14.3, Problem 86ES

Chapter 14.3, Problem 88ES

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Chapter 14 Solutions

EP ELEMENTARY+INTERMEDIATE ALG.-MYMATHA

Ch. 14.1 - Prob. 1YT Ch. 14.1 - Prob. 2YT Ch. 14.1 - Prob. 3YT Ch. 14.1 - Prob. 4YT Ch. 14.1 - Prob. 5YT Ch. 14.1 - Prob. 1CYU Ch. 14.1 - Prob. 2CYU Ch. 14.1 - Prob. 3CYU Ch. 14.1 - Prob. 4CYU Ch. 14.1 - Prob. 5CYU

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