Write an equation to describe the sequence below.Use n to represent the position of a term in the sequence,where n = 1 for the first term.

Question

5, -10, 20
Write your answer using decimals and integers.
an = __ (__)n-1

Answer 1

To determine the equation for the sequence 5, -10, 20, we first need to identify the pattern.

1. Identify the terms:

   • 1st term (n = 1): \( a_1 = 5 \)
   • 2nd term (n = 2): \( a_2 = -10 \)
   • 3rd term (n = 3): \( a_3 = 20 \)

2. Look for the pattern: Let's calculate the ratios between the terms:

• From \( a_1 \) to \( a_2 \): \[ \text{ratio} = \frac{-10}{5} = -2 \]

• From \( a_2 \) to \( a_3 \): \[ \text{ratio} = \frac{20}{-10} = -2 \]

This indicates that each term is multiplied by -2 to get the next term.

3. General formula: We can express \( a_n \) as follows:

   • The first term is \( 5 \).
   • Each subsequent term is obtained by multiplying the previous term by -2.

   Therefore, we can write the equation for the \( n \)-th term as: \[ a_n = 5 \cdot (-2)^{(n-1)} \]

So, the final answer is: \[ a_n = 5 \cdot (-2)^{(n-1)} \]