Chapter 7 Test

term

a number in a sequence

geometric sequence

a sequence in which new terms are created by multiplying the previous terms by the same value (common ratio) each time

general term

formula that relates each term to its term number or position in the sequence

recursive formula

formula that uses previous term(s) to generate the next term

sequence

ordered list of numbers

arithmetic sequence

sequence in which new terms are created by adding the same value (common difference) each time

Geometric series

the sum of the terms of a geometric sequence

series

the sum of the terms of a sequence

arithmetic series

the sum of the terms of an arithmetic sequence

*recursive formula for a geometric sequence

tn=the nth term a=first term n=term number r=common ratio

*recursive formula of arithmetic sequence

tn=the nth term a=first term n=term number d=common difference

*Write out the first 6 rows of Pascal's triangle

to do this, calculate the sum of pairs of consecutive terms in the previous row

*graph of geometric sequence

when graphed, a geometric sequence represents a discrete exponential function of the form f(n)=arⁿ⁻¹

graph of arithmetic sequence

when graphed, arithmetic sequences represent discrete linear functions (f(n)=dn+t₀) ∴ can be used to model problems that involve increases/decreases at a constant rate

Review questions

→pg.468 #3,4,5,7,8,9,14,15,16,17,18, 19abc,20,22,23 →pg.470 #7

for a binomial expansion of the form (a+b)ⁿ:

-the coefficients in the expansion correspond to the numbers in the nth row of Pascal's triangle -each term of the expansion is comprised of a coefficient, a power of "a", and a power of "b" -the degree of each term (sum of the exponents of "a" and "b") in the expansion is equal to n -the exponents of "a" in the expansion start at "n" and decrease by one down to 0 while the exponents of "b" start at 0 and increase by one up to "n"