Question

What is the explicit formula for this sequence?

Answer 1

The answer is a
i hope this helps

Answer 2

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,

$a_1=4\:,\:a_2=-8\:,\:a_3=16\:,\:a_4=-32$

Option A :

$a_n=2\times(-4)^n$

$a_1=2\times(-4)^1=-8$

$a_1$ of the sequence does not matches with the $a_1$ of the formula.

Thus, This option is incorrect.

Option B :

$a_n=4\times(-2)^{n-1}$

$a_1=4\times(-2)^{1-1}=4$

$a_2=4\times(-2)^{2-1}=-8$

$a_3=4\times(-2)^{3-1}=16$

$a_4=4\times(-2)^{4-1}=-32$

$a_1$ of the sequence matches with the $a_1$ of the formula.

Thus, This option is correct.

Option C :

$a_n=-2\times(4)^{n-1}$

$a_1=-2\times(4)^{1-1}=-2$

$a_1$ of the sequence does not matches with the $a_1$ of the formula.

Thus, This option is incorrect.

Option D :

$a_n=4\times(-2)^{n}$

$a_1=4\times(-2)^{1}=-8$

$a_1$ of the sequence does not matches with the $a_1$ of the formula.

Thus, This option is incorrect.

Therefore, Option B is correct.