M4 1. Write a paragraph at a level that a high school student would un-derstand that explains your procedure for approximating v7, andexplain (i.e., prove without using the word "proof") why the se-quences in your procedure converge to v7. Your procedure needsto be both (a) consistent and (b) iterative/infinite. Discuss whyeach of these two ideas is important for the sequences to convergeto a single number, and explain where in the proof of convergenceyou use consistency and where you use the iterative/infinite natureof the procedure.

The objective is to write a paragraph on approximating the irrational number 7.

Answered: 1. Write a paragraph at a level that a…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.1: Sequences And Their Notations

Problem 65SE: Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do...

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Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose ‘seq(” from the dropdown list. Press [ENTER] • In the line headed “Expr:” type in the explicit formula, using the [X,T,,n] button for n • In the line headed ‘Variable” type In the variable used on the previous step. • In the line headed ‘start:” key in the value of n that begins the sequence. • In the line headed “end:’ key in the value of n that ends the sequence. • Press [ENTER] 3 times to return to the home screen. You will see the sequence syntax on the screen. Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. Using a TI-83, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose “seq(“ from the dropdown list. Press [ENTER]. • Enter the items in the order “Expr’, Variable’, ‘start”. end separated by commas. See the instructions above for the description of each item. • Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary. 65. List the first four terms of the sequence. an=5.7n+0.275(n1)
Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose ‘seq(” from the dropdown list. Press [ENTER] • In the line headed “Expr:” type in the explicit formula, using the [X,T,,n] button for n• In the line headed ‘Variable” type In the variable used on the previous step. • In the line headed ‘start:” key in the value of n that begins the sequence. • In the line headed “end:’ key in the value ofnthat ends the sequence. • Press [ENTER] 3 times to return to the home screen. You will see the sequence syntax on the screen. Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. Using a TI-83, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose “seq(“from the dropdown list. Press [ENTER]. • Enter the items in the order “Expr’, Variable’, ‘start”. end separated by commas. See the instructions above for the description of each item. • Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary. 62. List the first five terms of the sequence. an=289n+53
Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose ‘seq(” from the dropdown list. Press [ENTER] • In the line headed “Expr:” type in the explicit formula, using the [X,T,,n] button for n • In the line headed ‘Variable” type In the variable used on the previous step. • In the line headed ‘start:” key in the value of n that begins the sequence. • In the line headed “end:’ key in the value of n that ends the sequence. • Press [ENTER] 3 times to return to the home screen. You will see the sequence syntax on the screen. Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. Using a TI-83, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose “seq(“ from the dropdown list. Press [ENTER]. • Enter the items in the order “Expr’, Variable’, ‘start”. end separated by commas. See the instructions above for the description of each item. • Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary. 66. List the first six terms of the sequence an=n!n
Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose ‘seq(” from the dropdown list. Press [ENTER] • In the line headed “Expr:” type in the explicit formula, using the [X,T,,n] button for n• In the line headed ‘Variable” type In the variable used on the previous step. • In the line headed ‘start:” key in the value of n that begins the sequence. • In the line headed “end:’ key in the value of nthat ends the sequence. • Press [ENTER] 3 times to return to the home screen. You will see the sequence syntax on the screen. Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. Using a TI-83, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose “seq(“ from the dropdown list. Press [ENTER]. • Enter the items in the order “Expr’, Variable’, ‘start”. end separated by commas. See the instructions above for the description of each item. • Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary. 63. List the first six terms of the sequence. an=n33.5n2+4.1n1.52.4n

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