Question

Determine whether each sequence is arithmetic or geometric. sequence 1: 32, 16, 0, –16, ... sequence 2: 32, 16, 8, 4, ...

Answer 1

S1.
32, 16, 0, -16, ...
It's an arithmetic sequence:

$a_1=32;\ d=16-32=-16\\\\a_n=a_1+(n-1)d\\\\a_n=32+(n-1)\cdot(-16)=32-16n+16=48-16n$

S2.
32, 16, 8, 4, ...
It's a geometric sequence:

$a_1=32;\ r=16:32=\dfrac{1}{2}\\\\a_n=a_1r^{n-1}\\\\a_n=32\cdot\left(\dfrac{1}{2}\right)^{n-1}$

Answer: sequence 1 is arithmetic and sequence 2 is geometric.