The sequence { g subscript n } is defined recursively as follows: g subscript 0 = 1, and g subscript n = 3 * g subscript n - 1 end subscript + 2 subscript n, for n greater or = than 1 .If the theorem below is proven by induction, what must be established in the inductive step?Theorem: For any non-negative integer n, g subscript n equals 5 over 2 times 2 to the power of n minus n minus 3 over 2 . The sequence {g} is defined recursively as follows:n80=1 andad 8 n = 3.8₁If the theorem below is proven by induction, what must be established in the inductive step?(A)5Theorem: For any non-negative integer n, g = 2" - n-.n2BⒸ(D)then gFor k ≥ 0, if g = 3·8 k-1 +2k,53= — . 2k +¹ − (k + 1) - 2/22k+1n-1then g+2₁, for n ≥ 1.n5For k ≥ 0, if g,20-2¹4-kk+1then gk+1-k-For k ≥ 0, if g = 3 ⋅8k_₁+2k,kk-153k+1= -√2₁ 2² + 1 - (K + 1) - 12/2= 3.g₁ +2(k+1).k5For k ≥ 0, if għ =2322k - k-then 8 = 3.3.8 +2(k+1).k+13232.

The principle of induction states that at inductive step to prove a statement P(n), we need to prove…

The sequence {g} is defined recursively as follows: n 80=1 and ad 8 n = 3.8₁ If the theorem below is proven by induction, what must be established in the inductive step? (A) 5 Theorem: For any non-negative integer n, g = 2" - n- . n 2 B Ⓒ (D) then g For k ≥ 0, if g = 3·8 k-1 +2k, 5 3 = — . 2k +¹ − (k + 1) - 2/2 2 k+1 n-1 then g +2₁, for n ≥ 1. n 5 For k ≥ 0, if g, 20-2¹4- k k+1 then g k+1 -k- For k ≥ 0, if g = 3 ⋅8k_₁+2k, k k-1 5 3 k+1 = -√2₁ 2² + 1 - (K + 1) - 12/2 = 3.g₁ +2(k+1). k 5 For k ≥ 0, if għ = 2 3 2 2k - k- then 8 = 3. 3.8 +2(k+1). k+1 3 2 3 2 .

The sequence {g} is defined recursively as follows: n 80=1 and ad 8 n = 3.8₁ If the theorem below is proven by induction, what must be established in the inductive step? (A) 5 Theorem: For any non-negative integer n, g = 2" - n- . n 2 B Ⓒ (D) then g For k ≥ 0, if g = 3·8 k-1 +2k, 5 3 = — . 2k +¹ − (k + 1) - 2/2 2 k+1 n-1 then g +2₁, for n ≥ 1. n 5 For k ≥ 0, if g, 20-2¹4- k k+1 then g k+1 -k- For k ≥ 0, if g = 3 ⋅8k_₁+2k, k k-1 5 3 k+1 = -√2₁ 2² + 1 - (K + 1) - 12/2 = 3.g₁ +2(k+1). k 5 For k ≥ 0, if għ = 2 3 2 2k - k- then 8 = 3. 3.8 +2(k+1). k+1 3 2 3 2 .

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter13: Sequences And Series

Section13.CT: Chapter Test

Problem 2CT

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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 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
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