Question

Which sequence is modeled by the graph below?

Answer 1

Answer:

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

Step-by-step explanation:

Check:

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

Answer 2

Answer:

$a_n=6\left(\frac{1}{10}\right)^{n-1}$

Option 3 is correct

Step-by-step 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:

$r=\dfrac{a_2}{a_1}=\dfrac{0.6}{6}=0.1$

Formula of geometric sequence:

$a_n=ar^{n-1}$

$a_n=6\cdot 0.1^{n-1}$

$a_n=6\left(\frac{1}{10}\right)^{n-1}$

Hence, The sequence model by $a_n=6\left(\frac{1}{10}\right)^{n-1}$