Tuesday 13 May class

(after Test 4)



• Sequences in general and some notation: introduction to arithmetic and geometric sequences

• Arithmetic sequences

• The general formula for the nth term of an arithmetic sequence: a_n = a_1 + d(n-1)

We multiply d by (n-1) because we start adding d when we go to the second term.

• Summation notation

• Finding the sum of the first k terms of an arithmetic sequence: \Sum_{i=1}^k a_i = \frac{k}{2}\left(a_1 + a_k\right) or k\left(\frac{a_1+a_k}{2}\right)

Use whichever form you find easiest to remember. To remember them more easily, recall how we derived the formula looking at Gauss’ trick for adding the first 100 natural numbers.



• Review the definitions and notation introduced today, and the examples discussed in class. Make sure that you understand how we derived the formula for the sum of the first k terms of an arithmetic sequence given above.

• Do the assigned parts of problems 23.1, 23.3, 23.4 and 23.5 : we will return to the summation of 23.7 next time, but you may want to try it.

• Do the WeBWorK (due next Monday by 11 PM, but start early!)

• Look over the Final Exam Review sheet (handed out in class or available from the link in the sidebar) and choose some problems you would want to present next week on review day. You will sign up for one problem next time, but there will be the opportunity to volunteer for more, so prepare as many as you can.


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