Question

Which sequence is modeled by the graph below? (1 point) coordinate plane showing the points 1, 5; 2, 0.5; and 3, 0.05 an = 5(−10)n − 1 an = 0.5(10)n − 1 an = one tenth (5)n − 1 an = 5( one tenth )n − 1

Answer 1

Answer:

$\large\boxed{a_n=5\left(\dfrac{1}{10}\right)^{n-1}}$

Step-by-step explanation:

Check:

$n=1\\\\a_1=5\left(\dfrac{1}{10}\right)^{1-1}=5\left(\dfrac{1}{10}\right)^0=5(1)=5\qquad\bold{CORRECT}\ (1,\ 5)\\\\n=2\\\\a_2=5\left(\dfrac{1}{10}\right)^{2-1}=5\left(\dfrac{1}{10}\right)^1=5\left(\dfrac{1}{10}\right)=\dfrac{5}{10}=0.5\qquad\bold{CORRECT}\ (2,\ 0.5)\\\\n=3\\\\a_3=5\left(\dfrac{1}{10}\right)^{3-1}=5\left(\dfrac{1}{10}\right)^2=5\left(\dfrac{1}{100}\right)=\dfrac{5}{100}=0.05\qquad\bold{CORRECT}\ (3,\ 0.05)$