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A: Topic = Sequence
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Q: 2)Define the sequence: a, = (n+1)! (n = 1,2,3, ...) recursively. %3D
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Q: Find an explicit formula for a sequence of the form a1, a2, a3,
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A: Let's find first six terms of the recursive sequence.
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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…
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Q: 4. Give a recursive definition of the sequence an if an = n(n+1), where n = 1, 2, 3, ... %3D
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A: find Your Solution Below
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Q: Suppose the sequence {an} is defined by the explicit formulaan = 1/n, for n = 1, 2, 3, ⋅ ⋅ ⋅. Write…
A: Given:an=1n, n=1,2,3.........a1=?a2=?a3=?a4=?a5=?
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Q: Let an be a sequence defined by a1 = 0 and a2 = 1 and for n > 3 an = (n – 1)(an-1+an-2). %3D
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Q: write an expression for the apparent nth term (an) of the sequence and assume that n begins with 1…
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Q: c) Write the explicit formula for the nth term of the sequence below. d) Prove that mathematical…
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Q: Find an explicit formula for a sequence of the form a1, a2, a3, with the initial terms given…
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Q: Determine whether each sequence having the given nth term is monotonic. a. a, = 3+ (-1)"
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Q: Show that if a and x are any two nonzero real numbers, then ,-1,,-.. is a geometric sequence.
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Q: Suppose that a sequence is defined as follows. a1 =-4, an= 3a,-1+7 n2 2 for List the first four…
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Q: Give a recursive definition of the sequence {an}, n = 1, 2,... if: a. an=4n-2 b. an=1+ (-1)"
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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…
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A: first we write few terms of given sequence then observe the pattern to get final answers.
Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…
A: Given sequence is: 5,12,19,26,33,...
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- The second term of a geometric sequence is 14, and the sixth term is 224. Find the nth term. (Assume that the terms of the sequence are positive.)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
- 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+4.1n1.52.4nConsider the sequence defined by an=68n. Is an=421 a term in the sequence? Verify the result.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.
