Question

The question is: type your equation for the following pattern

Answer 1

Answer:

$\large\boxed{a(n)=16\left(\dfrac{1}{2}\right)^{n-1}}$

Step-by-step explanation:

$a(1)=16\\\\a(2)=16:2=8\\\\a(3)=8:2=4\\\\a(4)=4:2=2\\\\a(5)=2:2=1\\\\a(n)=a_{n-1}:2=\dfrac{1}{2}a_{n-1}$

This is a geometric series with the common ratio $r=\dfrac{1}{2}$ and the first term $a_1=16$.

An explicit formula of the n-th term of a geometric sequence:

$a_n=a_1r^{n-1}$

Substitute:

$a_n=16\left(\dfrac{1}{2}\right)^{n-1}$