Answer:
Option B is correct.
Step-by-step explanation:
Given Sequence is:
4 , -8 , 16 , -32 , ...
To find: Explicit formula for the sequence.
From give sequence,
[tex]a_1=4\:,\:a_2=-8\:,\:a_3=16\:,\:a_4=-32[/tex]
Option A :
[tex]a_n=2\times(-4)^n[/tex]
[tex]a_1=2\times(-4)^1=-8[/tex]
[tex]a_1[/tex] of the sequence does not matches with the [tex]a_1[/tex] of the formula.
Thus, This option is incorrect.
Option B :
[tex]a_n=4\times(-2)^{n-1}[/tex]
[tex]a_1=4\times(-2)^{1-1}=4[/tex]
[tex]a_2=4\times(-2)^{2-1}=-8[/tex]
[tex]a_3=4\times(-2)^{3-1}=16[/tex]
[tex]a_4=4\times(-2)^{4-1}=-32[/tex]
[tex]a_1[/tex] of the sequence matches with the [tex]a_1[/tex] of the formula.
Thus, This option is correct.
Option C :
[tex]a_n=-2\times(4)^{n-1}[/tex]
[tex]a_1=-2\times(4)^{1-1}=-2[/tex]
[tex]a_1[/tex] of the sequence does not matches with the [tex]a_1[/tex] of the formula.
Thus, This option is incorrect.
Option D :
[tex]a_n=4\times(-2)^{n}[/tex]
[tex]a_1=4\times(-2)^{1}=-8[/tex]
[tex]a_1[/tex] of the sequence does not matches with the [tex]a_1[/tex] of the formula.
Thus, This option is incorrect.
Therefore, Option B is correct.
