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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.

Respuesta :

dalendrk
S1.
32, 16, 0, -16, ...
It's an arithmetic sequence:
[tex]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[/tex]

S2.
32, 16, 8, 4, ...
It's a geometric sequence:
[tex]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}[/tex]

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

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