Determine whether each of the following sequences (an) converges, and find the limit of each convergent sequence. Name any results or rules tha you use. You may use the basic null sequences listed in Theorem D7 from Unit D2. (a) an - (b) an = (c) = 4(2) + 3n¹ +6 3(2n)+n4+2n³' n5 + 3n² + 2n 4n4 + 2n²-n' n = 1, 2, ... n = 1, 2, ... n²+3n² + 2(n!) n³ + 2n² + (−1)n(n!)' n = 1, 2, ...

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

Find the 12th term of the geometric sequence whose first term is 14 and whose common ratio is 1.2.

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 16th partial sum of the arithmetic sequence 6, 18, 30, 42, . . . .

At which term does the sequence 10,12,14.4,17.28,... exceed 100?

At which term does the term does the sequence 5.4,14.5,23.6, exceed 151?

Find the next term of each sequence 1, 6, 11, 16,

Describe three ways that a sequence can be defined.