Question

What is the recursive rule for this geometric sequence?

Answer 1

Answer:

Step-by-step explanation:

A geometric sequence is defined as the sequence of number that follows  a pattern were the next term is found by multiplying by a constant called the common ratio say r.

The recursive rule is given by;

$a_n = r \cdot a_{n-1}$ where n is the number of terms.

Given the sequence: $-64, -16, -4 , -1, ....$

This sequence is a geometric sequence with common ratio (r) = $\frac{1}{4}$

Here, first term $a_1 = -64$

Since,

$\frac{-16}{-64} = \frac{1}{4}$

$\frac{-4}{-16} = \frac{1}{4}$ and so on....

The recursive rule for this sequence is;

$a_n = \frac{1}{4} \cdot a_{n-1}$

Answer 2

$a_n=\left\{\begin{array}{ccc}a_1=-64\\a_{n+1}=a_n:4\end{array}\right\\\\check:\\a_1=-64\\a_2=a_1:4\to a_2=-64:4=-16-OK\\a_3=a_2:4\to a_2=-16:4=-4-OK\\a_4=a_3:4\to a_4=-4:4=-1-OK\\\vdots$