Calculations. For each sequence, explain whether it is conver- gent, divergent to t∞, or otherwise divergent (not to ±x). If it is convergent, find its limit. 3 n→∞ 2-ni (a) lim (b) lim x-2 x²4 x + 4

Find the 5thterm of the geometric sequence {b,4b,16b,...}.

Use the explicit formula to write a geometric sequence whose common ratio is a decimal number between 0 and 1. Show the first 4 terms, and then find the 8th term.

What is the 11thterm of the geometric sequence 1.5,3,6,12,... ?

Find the next term of each sequence 1, 3, 6, 10,.

Use the recursive formula to write a geometric sequence whose common ratio is an integer. Show the first four terms, and then find the 10thterm.

Find the sum of the first five terms of the sequence with the given general term. an=3n2

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.

An arithmetic sequence is a sequence in which the ___________ between successive terms is constant.

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