Question

Consider the sequence:

Answer 1

Answer:

The 7th number in the sequence is $\frac{125}{8}$

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio.

The nth term of a geometric sequence is given by:

$A_n = A(0)r^{n-1}$

In which A(0) is the first term and r is the common ratio.

1000,-500,250,-125

This means that $A(0) = 1000, r = -\frac{500}{1000} = -\frac{1}{2}$

So

$A_n = A(0)r^{n-1}$

$A_n = 1000(-\frac{1}{2})^{n-1}$

What is the 7th number in the sequence?

This is $A_7$. So

$A_7 = 1000(-\frac{1}{2})^{7-1} = \frac{1000}{64} = \frac{125}{8}$

The 7th number in the sequence is $\frac{125}{8}$