Question

What is the explicit formula for this sequence?

Answer 1

the answer is a
i hope this helps

Answer 2

Option B is correct.

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*(-4)^n`

`a_1=2*(-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*(-2)^(n-1)`

`a_1=4*(-2)^(1-1)=4`

`a_2=4*(-2)^(2-1)=-8`

`a_3=4*(-2)^(3-1)=16`

`a_4=4*(-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*(4)^(n-1)`

`a_1=-2*(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*(-2)^(n)`

`a_1=4*(-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.