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Sequences Preliminary instructions In this lab, we will learn to: 1. Use Excel to evaluate the terms of an arithmetic sequence 2. Use Excel to

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Sequences Preliminary instructions In this lab, we will learn to: 1. Use Excel to evaluate the terms of an arithmetic sequence 2. Use Excel to evaluate the terms of a geometric sequence 3. Use Excel's autolill feature 4. Format cells. Recall some basics about sequences: I An arithmetic sequence is a sequence dened by a common differenced, where ' u :anil +63 :dn+o (71+ 1)(an + a\") - the nth partial sum of an arithmetic sequence isS,1 = 2 I A geometric sequence is a sequence dened by a common ratior, where - an = (11171-7 = an?\" 131+] 7 1 - the nth partial sum of a geometric sequence isSn : an 1 ,n 7 Since Excel is good at repeating patterns. we will use it to list out the terms of a sequence and find the corresponding partial sums. For the arithmetic sequence example, we will use Excel to construct the first 100 terms and 100 partial sums of the sequence {3.4.5.6.7.5.9,1G.5,...}. Step 1: Setup the table for the sequence I Start by lilling in the cells A8 through A108 with the numbers 0 through 100 (U in A8. 1 in A9. 100 in A103). Use Excel's autolill feature by lling in the rst two numbers. highlighting A8 and A9. and then dragging down to A10? with the black plus sign in the bottom right corner. I Make the rst term of the arithmetic sequence 3 by entering 3 in cell ()4. I Make the common difference 1.5 by entering 1.5 in cell C5. Step 2: List the terms of the sequence I In cell B8. type "=C4" (without the quotation marks). - This tells Excel that B8 is equal to the value in C4. I In cell B9 type \":BS+3CEB". and then autoll to the last term of the sequence. - Notice that the $'s lock the cell C5, so that it does not change during the autofill. - Notice we are using + because we are addingthe common difference. Step 3: Evaluate the nth partial sums I In cell C8 type "=B8\". I In cell CQ type ":C8+B9". and then autoll to the last term of the sequence. This makes C9 (the current sum) = C8 (the previous sum) + B9 (the current value). I Highlight 09 and autolill to the last term of the sequence. That's it! 11' you have mm = 153 (or cell 3108 is 153) and if you haveSmn = 7878 (or cell C108 is 7878), you have done everything correctly. Notice that we can easily change the sequence. Let's make the first term 5 and common difference 2 by changing C4 to 5 and C5 to 2. If C108 is 10605, your Excel lile is working correctly. Now. try to do something similar for the geometric sequence {3,4.5,6.75,1U.125.15.1875. ....} ((10 = 3.1- = 1.5). El" you follow the same steps as in the last example, you should get ' G100 =1.21958 X1018 - sum 2 3.65905 x 10\

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