Question

Which choice is the explicit formula for the following geometric sequence

Answer 1

Hello,

2/10,-6/100,18/1000,-54/10000,162/100000;...


a(n+1)/a(n)=-3/10
a(0)=2/10*1

a(n)=2/10* (-3/10)^(n-1)

Answer B

Answer 2

B:
`a_n= 0.2(-0.3)^(n-1)`

Explanation:

Geometric sequence

0.2, -0.06, 0.018,-0.0054,0.00162....

General explicit formula is
`a_n= a_1(r)^(n-1)`

Where r is the common ratio and a1 is the first term

a1 is 0.2 (first term)

we need to find out common ratio 'r'

To find 'r' divide second term by first term

`(-0.06)/(0.2) =-0.3`

Plug in the values in the general formula

`a_n= a_1(r)^(n-1)`

`a_n= 0.2(-0.3)^(n-1)`