Geometric Sequence Please show work so I can understand 1 42

Geometric Sequence       Please show work so I can understand

1. 4,2,1,... Find a10

2. 5, 15/2, 45/4,.... Find a8

3. 6, -2, 2/3,... Find a12

4. 1, -2/3, 4/9,... Find a7                                                                 

5. 100,200,400,... Find a9

6. 8,32,128,... Find a4

Solution

nth term of gp is given by:

an = a1*r^(n - 1)

an . = nth term

a1 = first term

r = common ratio

A.

4, 2, 1

a10 = 4*(1/2)^(10 - 1) = (1/2)^7

B.

5.15/2, 45/4

a8 = 5*(3/2)^7

C.

6, -2, 2/3

a12 = 6*(-1/3)^11 = -2/3^10

D.

1, -2/3, 4/9

a7 = 1*(-2/3)^6 = 2^6/3^6

E.

100, 200, 400....

a9 = 100*(2)^8

a9= 2^8*100

6.

8, 32, 128....

a4 = 8*4^3 = 512