Question

Determine whether the sequence is arithmetic or geometric.

sequence 1: 32, 16, 0, –16, ...
sequence 2: 32, 16, 8, 4, ...
which of the following statements are true regarding sequence 1 and sequence 2.

sequence 1 is arithmetic and sequence 2 is geometric.
both sequences are arithmetic.
both sequences are geometric.
sequence 2 is arithmetic and sequence 1 is geometric.

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=(1)/(2)\\\\a_n=a_1r^(n-1)\\\\a_n=32\cdot\left((1)/(2)\right)^(n-1)`

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