Question

Which sequence is modeled by the graph below?

coordinate plane showing the points 1, 6; 2, 0.6; and 3, 0.06

Answer 1

`\large\boxed{a_n=6\left((1)/(10)\right)^(n-1)}`

Explanation:

Check:

`n=1\\\\a_1=6\left((1)/(10)\right)^(1-1)=6\left((1)/(10)\right)^0=6(1)=6\qquad\bold{CORRECT}\ (1,\ 6)\\\\n=2\\\\a_2=6\left((1)/(10)\right)^(2-1)=6\left((1)/(10)\right)^1=6\left((1)/(10)\right)=(6)/(10)=0.6\qquad\bold{CORRECT}\ (2,\ 0.6)\\\\n=3\\\\a_3=6\left((1)/(10)\right)^(3-1)=6\left((1)/(10)\right)^2=6\left((1)/(100)\right)=(6)/(100)=0.06\qquad\bold{CORRECT}\ (3,\ 0.06)`

Answer 2

`a_n=6\left((1)/(10)\right)^(n-1)`

Option 3 is correct

Explanation:

The coordinates are (1,6) (2,0.6) and (3,0.06)

If we make table of given coordinate:

x : 1 2 3

y : 6 0.6 0.06

`a_1=6,a_2=0.6,a_3=0.06`

Ratio of the sequence:

`r=(a_2)/(a_1)=(0.6)/(6)=0.1`

Formula of geometric sequence:

`a_n=ar^(n-1)`

`a_n=6\cdot 0.1^(n-1)`

`a_n=6\left((1)/(10)\right)^(n-1)`

Hence, The sequence model by
`a_n=6\left((1)/(10)\right)^(n-1)`