@article {MATHEDUC.06520645, author = {Davis, Marsha}, title = {Modeling with sequences.}, year = {2015}, journal = {Consortium}, volume = {108}, issn = {0889-5392}, pages = {17 p., pull-out section}, publisher = {COMAP (Consortium for Mathematics and Its Applications), Bedford, MA}, abstract = {From the text: In Activity 1, students use two types of sequences to model population growth over time. The assumption that population grows by a constant amount each year leads to an arithmetic-sequence. A more realistic assumption that population grows by a constant annual percentage leads to a geometric sequence. The context in Activity 2 is credit-card debt. In the first scenario, no interest is charged and the \\$ 200 payments lead to debt balances that form an arithmetic sequence. In the second scenario, interest is charged on the balance. In this case, the debt balances form a mixed sequence (a combination of arithmetic and geometric sequences). In Activity 3, students work with sequences that describe the rows of Pascal's triangle. A search for efficient formulas to calculate various terms in Pascal's triangle leads to several of Pascal's identities, which appear in his ``Treatise on the Arithmetical Triangle". Finally, the connection is made between the terms in the \$n\$th row of Pascal's triangle and combinations ``\$n\$ choose \$k\$" for \$k=0\$,\dots \$n\$. Then, students use the rows of Pascal's triangle to construct probability models for the number of heads in \$n\$ flips of a coin.}, msc2010 = {D80xx (I30xx K20xx M10xx)}, identifier = {2016a.00420}, }