We covered Arithmetic Series today.
When we add a group of consecutive terms of an arithmetic sequence, we form an arithmetic series. For an arithmetic sequence with the first term as a and the common difference d, the sum of the first n terms of the sequenece is:
Sn = n(a1 + an)/2
That is, the sum is the average of the first and last terms, times the number of terms. We want the students to understand how we get to that formulae, not just memorize it (which is the least they should do).
We did quite some in-class exercises mixing the arithmetic sequence formulae for the nth term and the sum of the first n terms. Usually the steps go like this: first figure of how many terms we are talking about, then see if we have the first term and the last term, if so, we can already find the sum; if not, look at the givens and figure out the first term and the common difference.
Another set of problems usually give two conditions about some terms in an arithmetic sequence. Because we want to find out a and d, two conditions usually is all we need to find the unknown of a and d. With a and d, we can find any term in an arithmetic sequnce.
Homework is the following:
http://www.newtonchineseschool.org/teachers/wangweidong/HomeworkArithmeticSeries.pdf
