Sequences

recursive formula always gives what information

1. the first term of the sequence 2. the common difference

which is true of geometric sequence 1. common difference 2. form line graph 3. model exponential function 4. add/subtract to get next term

3 1 wrong because they have a common ratio 2. wrong because they form curved line (exponential) 4. wrong because you multiply or divide to get next term

given the first term 3 and the common difference 5 what are the 1st 5 terms

3 3+5 = 8 8+5 = 13 13 + 5 =18 18 + 5 = 23

given the first term 4 and common ratio -2 find the 1st 5 terms

4 4 * -2 = -8 -8 * -2 = 16 16 * -2 = -32 -32 * -2 = 64

which represents a linear function 1, 3, 9, 27 9, 3, 1, 1/3 4, 8, 12, 16 4, 8, 16, 32

4, 8, 12, 16 because its arithmetic (add 4 )

duck population starts with 7 ducks and doubles every year. How many ducks will be in the population after 9 years

7 * (2) 9th power 7 * 512 3584

arithmatic sequence

a sequence in which each term is found by adding or subtracting the same number from the previous term form line graph common difference not common ratio

geometric sequence

a sequence in which each term is found by multiplying the previous term by the same number. Form exponential function (curved graph) common ratio not common difference

show 4, -16, 64, -256, 1024 recursively

a1 = 4 and a(n) = -4a (n-1) 4 is 1st term -4 is common ratio

recursive formula

always have 1st term and common difference

new school is adding 50 students each year this is an example of geometric growth geometric decay arithmetic growth arithmetic decay

arithmetic growth know this because it says adding and it is getting bigger

how to write explicit formula

first term + common difference(n-1)

2, 6, 18, 54, 162 is this geometric, arithmetic, or neither and what is the common difference or ratio

geometric (because its multiplied not added/subtracted) common ratio = 3 3x2 = 6, 6x2=18, 18x2=54, 54x2=162

how to know if a sequence represents a linear function

if there is a constant rate of change

ratio

multiplication

explicit formula

plug term you are looking for as n always written as A + B(n-1) A =1st term and B = common difference

a(n-1) in recursive formula

the term before the term you are looking for ( so basically for a(n) take the answer of the term before the one you are looking for and add the common difference)

rabbit population starts with 10 rabbits and doubles each year for three years. How many rabbits after 3years

y = 10*(2) 3rd power 10(8) 80

12, 36, 108, 324 what formula represents

y = 12*3xpower 1st term =12 common ratio = 3

a bacteria colony starts with 5 bacteria and triples every hour. what equation models the situation

y = 5 * 3 x power

7, 14, 28, 56, 112, 224 equation for this sequence

y = 7(2)x power 1st term is 7 common ratio is 2