Discrete Functions

Explicit Formula

100

Write the first 3 terms of each sequence. tn=4n-3

t1=1

t2=5

t3=9

200

Write the explicit Formula for the nth term and the first 3 terms 

4, 7, 10, 13, 16

Tn= 3n+1

T1= 3(1)+1=4

T2= 3(2)+1=7

T3= 3(3)+1=10

300

Write the explicit formula for the first 3 terms and 10th term.

F(n)= n²+4

T₁₌5

T₂= 8

T₃= 13

T₁₀₌ 104

400

Determine the explicit formula for the nth term and the first 5 term

3, 7, 11, 15, 19 

Tn= 4n-1                T₅=4(5)-1 = 19

T₁= 4(1)-1 = 3

T₂= 4(2)-1 = 7

T₃= 4(3)-1 = 11

T₄= 4(4)-1 = 15

500

Determine the first 3 terms and then use the formula to find t₅₈

3, 8, 13, 18, 23

T_n= 5n-2           T₅₈=5(58)-2=288

T₁₌5(1)-2 = 3

T₂₌ 5(2)-2 = 8

T₃=5(3)-2 = 13

Recursion

100

Write the first 3 terms of each sequence.

t₁=3   t_n= t_n-1-2

t₁= 3

t₂=1

t₃= -1

200

Write the first 5 sequence

t₁= 7       t_n= t_n-1+8

t₁₌7

t₂= 15

t₃=23

t₄= 31    t₅= 39

300

Write the first 4 terms of the sequence.

t₁= 2, t_n= 2t_n-1+ 3n

t₁= 2

t₂ = 10

t₃ = 29

t₄= 70

400

Determine the recursion formula for the sequence.

15, 22, 29, 36...

t₁=15, t_n= t_n-1+7

500

Write the first four terms in each sequence.

t₁= 3, t₂= 6

t_n= (t_n-1)-4t_n-2

t₁=3

t₂= 6

t₃= -72

t₄= 1728

Sequences

100

Find the formula for the nth term

5, 25, 125, 625

t_n= 5(5)^n-1

200

How many terms are there in the following sequencetn

14, 11, 8, 5..-40

tn= a(n-1)d         -23=-3n

=14+(n-1)-3         n= 7.66=8 terms.

=-3n+17               

-40=-3n+17

300

Find how many terms there in this sequence.

4, 8, 12, 16...28

tn=4+(n-1)(4)     n=7 terms

tn= 4+ 4n -4

tn = 4n

28=4n

400

Find the formula for the nth term, and t₈

2,5,8, 11...

tn= 2(3)^n-1

tn= 2(3)^8-1

tn= 4374

500

Find the general formula for an arimethic sequence with t₁₀₌-16, and t₁₆= 34

d= 34-(-16)           50

      _______       ______    =8.3=8         -16=a(10-1)(8)

     16-10                6                              -16=a+72

                                                              -88=a

     

Series

100

Find the sum of the first 30 terms of each series

10, 14, 18, 22...

S₃₀=30   [2(10)+(30-1)4            S₃₀=15(136)

      ___                                      S₃₀= 2040

        2

200

Find t₄₀ of each series.

-3-6-12-...

S₆₀= -3(2⁶⁰-1)    = -3.4587x10¹⁸

       _______    

           2-1

300

Find t₅₀ of each sequence

9+27+81+162...

Sn= 9[3⁵⁰-1]    Sn= 3.2305x10²⁴

       _______

           3-1

400

Car value depresiates by 20% each year. If the original cost is 58000, what will its value be at the end of 12 years

A=58000(0.80)^t                       

A=58000(0.80)¹²                     DO SERIES 500 NEXT

A= 3985.730  

500

After how many years will it be worth less than half of its original cost of 58000 

58000(0.80)^t

29000=58000(0.80)^t              log 0.5                 t=3.1 years 

0.5=0.80^t                                   ______=t      

                                         log 0.80

Definitions

100

What is a Recursion Formula

A sequence that is said to be recursive when a new term is found using a previous term or terms.

200

What is the definition of a Discrete Function? 

A discrete function is a function with distinct and separate values.

300

What is the defintion of a sequence

A set of number, shapes, o letter that are separeted by commas, and are arranged in a particular order.

400

What is the definition of an Explicit Formula?

A formula that represents any term in a sequence relative to the term number.

500

What is the defintion of a series

The sum of the terms in a Sequence