Sequences and Series

Arithmetic Sequences

100

Is this a Arithmetic Sequence yes or no?

1, 4, 7, 10 

yes

Calculations: follows a adding 3 pattern

200

Is this a Arithmetic Sequence yes or no?

10, 20, 40 

no

Calculations: does not follow a adding or subtracting pattern

300

what is the 10th term in this Arithmetic Sequence 

7, 11, 15, 19 

43

Calculations: 4(10) +3 = 43

400

Can 428 be a term is this Arithmetic Sequence? yes or no? if so what term is it?

-10, -4, 2, 8

yes and 74th term

Calculations: 

428 = 6n-16

444=6n

74=n

Geometric Sequences

100

Is this a Geometric Sequence yes or no?

1, 2, 4 , 8 , 16 

yes

Calculations: follows a multiplying pattern

200

Is this a Geometric Sequence yes or no?

81, 27, 9, 3 , 1, 1/3

yes

Calculations: Follows a dividing pattern

300

what is the 10th term in this Geometric Sequence 

625, 125, 25, 5 

0.00032 or 1/3125

Calculations: 625(1/5) ^10-1=0.00032 or 1/3125

400

Can 8196 be a term of this Geometric Sequence? yes or no? If so what term is it?

2, 4 ,8, 16

no

Calculations: no terms equal 8196

2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384, 32768 

Arithmetic Series

100

What is the Summation Notation from the 4th term to the 10th term given this Arithmetic Sequence 

19, 31 , 43

637

Calculations:

 ((10/5)(19+127))-((3/2)(19+43))=637

200

Given

t(n)=4n-2

Does 338= S₁₃ 

_{yes or no}

yes

Calculations: 338=(13/2)(2+50)

300

Given this Arithmetic sequence 

90 , 73, 56, 39

find S₁₅

-435

Calculations: (15/2)(90+-148)=-435

400

Given the Arithmetic Sequence:

-6, 7, 20, 33

what is S₃₀    

5475

Calculations: (30/2)(-6+371)=5475

Geometric Series

100

Given 

256, 64, 16 ,4 ,1 , 1/4 ,1/16

find S₄₀

341.3333333...

Calculations:  (256(1-(1/4)⁴⁰))/(1-(1/4)=341.333...

200

422(1/5)ⁿ

Find S₂₀

105.5

Calculations:(84.4(1-(1/5)²⁰))/(1-(1/5))=105.5 

300

Given the Geometric Sequence 

6, 36, 216

what is the S∞

∞

Calculations: Rate is over 1 if the rate is over 1 then S∞=∞

400

243(1/3)ⁿ

find S_∞

121.5

Calculations:81/(1-(1/3))=121.5

Recursive and Explicit equations

100

What is the explicit equation of this geometric sequence 

-1, 1 ,-1 , 1

t(n)=(-1)ⁿ

Calculations: n^th/n-1^th=r

1/-1=-1

r=-1

200

what is the Explicit Equation of this Arithmetic Sequence 

9, 14, 19, 24

t(n) =5n+4

Calculations: c.d.= n^th-(n-1)^th

14-9=5

5= c.d.

300

Find the recursive equation of this Geometric Sequence

1/2, 1/4, 1/8 

t(n+1)=1/2(t(n))

Calculations: n^th/n-1^th=r

(1/4)/(1/2)=0.5

r=.5

400

What is the explicit equation of this geometric sequence

5, 2.5, 1.25, .625 

t(n)=10(1/2)ⁿ

Calculations:  n^th/n-1^th=r

2.5/5=.5       r=.5