CPhill

This is a geometric series

The first term =  5

The common ratio is -2

The sum of the first five terms is

first term [  1 - common difference^5] / [ 1 - common difference ]

5  [ 1 - (-2)^5 ] / [ 1 - (-2) ]  =

5 [ 1 + 32 ]  / [ 3]  =

5 { 11]  = 

55

Area_sector  =  (1/2) radius^2  * ( theta in radians)

So

(1/2) (2)^2 ( pi/3)  =

(2/3) pi   cm^2

We have a geometric series......the sum of the first 6 terms is

first term [ 1 - common ratio^n ] / [ 1 - common ratio  ]       

Where n  = 6   and the common ratio  =  2

So  we have

8 [ 1 -  2^6] / [ 1 - 2 ]  =

8 [ -63] / -1  =

8 * 63  =

504 

a_n= 5(-2)^n-1

Recursive rule :

an = (-2) a_n-1        a₁  = 5

Thanks, Rom.....there is one more value of k......

If the discriminant is 0, we also have a rational solution  (root)

So

10^2 -  4k^2  = 0

100 = 4k^2

25  = k^2

5 = k 

We have a geometric series.....the common ratio   is    16/ - 8  = -2

The sum of the first n terms is given by:

first term  [  1 -  common ratio^n  ] / [ 1  - common ratio ]         

So.....the  sum is

-8 [ 1 - (-2)^(7) ] / [ 1 - (-2) ]  =

-8 [  1  -  (-2)^7]  / [ 3 ]   =  

-8 (129) / 3  =

-8 ( 43)  =

-344

2c: Why is the AA Postulate not likely to be the tool Quincy needs? (2 points)

Without knowing the length of JL.....we cannot determine any of the angles in triangle JKL

4.80 x 10²

First one :

a_n  = (2/5)(5)^{n - 1}

Recursive rule  :   a₁  = 2/5       a_n  =  5a_n-1 

Second one :

a₁ = 2         an  =  (1/3)a_n-1

Explicit Rule :     a_n  =  2(1/3)^n-1

Third one 

6, -18, 54, -162        [ note that the common ratio = -3 ]

Recursive Rule :    a₁  = 6        a_n  =  (-3)a_n-1

Fourth one :  9, 6,  4, 8/3

The common ratio is   :     6 / 9    =  2/3

Explicit Rule :    a_n  = 6(2/3)^n-1 

Note that   angle BAX   =  90  =   sum  of angle ABY  + angle BYA

So...

90  =  45 + angle BYA    subtract 45 from both sides

45 =  angle BYA  =  angle ABY

Su....triangle ABY is a 45 - 45 - 90  right triangle.....so the ratio of the sides   =

AB : AY :  BY  =     

1 : 1 :  sqrt (2)