need help Suppose that for f₁, f₂fo=is a sequence defined as follows.= 165, f₁ = 16,= 7fk - 110fkProve that f= 3 - 2ª + 2 · 5″ for each integer n ≥ 0.Proof by strong mathematical induction: Let the property P(n) be the equation f = 3.2" +2.5".We will show that P(n) is true for every integer n ≥ 0.Show that P(0) and P(1) are true:Select P(0) from the choices below.O P(0) = 3.20 +2.5⁰O P(0) = foTo = 5O f = 3.20 +2.5⁰- 2Select P(1) from the choices below.O P(1) = f₁OP(1) = 32¹ + 2 · 5¹f₁ = 3.2¹ +2 5¹f₁P(0) and P(1) are true because 3 20 +2.50 = 5 and 3 · 2¹ + 2.5¹ = 16.Show that for every integer k ≥ 1, if P(i) is true for each integer i from 0 through k, then P(k+ 1) is true:for every integer k ≥ 2Now, by definition of fo, f₁, f₂,fk+ 1 =Let k be any integer with k ≥ 1, and suppose that for every integer i with 0 ≤ i ≤ k, f; =Apply the inductive hypothesis to fk and fk - 1This is the --Select---and complete the proof as a free response. (Submit a file with a maximum size of 1 MB.)We must show that f+1=

Mathematical induction:For all-natural numbers, the principle of mathematical induction is a concept…

Suppose that for f₁ f2. is a sequence defined as follows. fo= 5, f₁ = 16, fk = 7fk-1-10fk - 2 for every integer k ≥ 2 Prove that f= 3.2" +2.5" for each integer n ≥ 0. Proof by strong mathematical induction: Let the property P(n) be the equation f 3.2" +2.5". = We will show that P(n) is true for every integer n ≥ 0. Show that P(0) and P(1) are true: Select P(0) from the choices below. OP(0) = 3.20 +2.5⁰ ○ P(0) = fo Of=5 Of=3.20 +2.5⁰ Select P(1) from the choices below. O P(1) = f₁ OP(1) = 3.2¹ +2.5¹ Of₁ = 3.2¹+2.5¹ O f₁ = 16 P(0) and P(1) are true because 3-20 +2.505 and 3.2¹ +2.5¹ = 16. Show that for every integer k ≥ 1, if P(i) is true for each integer i from 0 through k, then P(k + 1) is true: Let k be any integer with k ≥ 1, and suppose that for every integer i with 0 ≤ i ≤k, f, = . This is the ---Select--- Now, by definition of for f₁ f₂. fk+1= Apply the inductive hypothesis to f and fk - 1 and complete the proof as a free response. (Submit a file with a maximum size of 1 MB.) v We must show that fk + 1 =

Suppose that for f₁ f2. is a sequence defined as follows. fo= 5, f₁ = 16, fk = 7fk-1-10fk - 2 for every integer k ≥ 2 Prove that f= 3.2" +2.5" for each integer n ≥ 0. Proof by strong mathematical induction: Let the property P(n) be the equation f 3.2" +2.5". = We will show that P(n) is true for every integer n ≥ 0. Show that P(0) and P(1) are true: Select P(0) from the choices below. OP(0) = 3.20 +2.5⁰ ○ P(0) = fo Of=5 Of=3.20 +2.5⁰ Select P(1) from the choices below. O P(1) = f₁ OP(1) = 3.2¹ +2.5¹ Of₁ = 3.2¹+2.5¹ O f₁ = 16 P(0) and P(1) are true because 3-20 +2.505 and 3.2¹ +2.5¹ = 16. Show that for every integer k ≥ 1, if P(i) is true for each integer i from 0 through k, then P(k + 1) is true: Let k be any integer with k ≥ 1, and suppose that for every integer i with 0 ≤ i ≤k, f, = . This is the ---Select--- Now, by definition of for f₁ f₂. fk+1= Apply the inductive hypothesis to f and fk - 1 and complete the proof as a free response. (Submit a file with a maximum size of 1 MB.) v We must show that fk + 1 =

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 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
Calculate the first eight terms of the sequences an=(n+2)!(n1)! and bn=n3+3n32n , and then make a conjecture about the relationship between these two sequences.
Find the sum of the first five terms of the sequence with the given general term. an=3n2
Find a formula for the nth term of the arithmetic sequence whose common difference is 5 and whose first term is 1
Consider the sequence defined by an=68n. Is an=421 a term in the sequence? Verify the result.