Question

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. -135 , 45 , -15 , ... Write your answer using decimals and integers.

Answer 1

Step-by-step explanation: To write an equation that describes the given sequence, let's first analyze the pattern.

The sequence starts with -135, and each subsequent term is obtained by dividing the previous term by -3.

So, we can write the equation for the nth term of the sequence as:

a_n = (-135) * (-3)^(n-1)

In this equation, a_n represents the nth term of the sequence, and (-3)^(n-1) represents the exponent of -3, which increases by 1 with each subsequent term.

Let's verify this equation by plugging in the values of n to find the corresponding terms:

For n = 1:

a_1 = (-135) * (-3)^(1-1) = -135 * (-3)^0 = -135 * 1 = -135

For n = 2:

a_2 = (-135) * (-3)^(2-1) = -135 * (-3)^1 = -135 * (-3) = 405

For n = 3:

a_3 = (-135) * (-3)^(3-1) = -135 * (-3)^2 = -135 * 9 = -1215

The calculated values match the given sequence: -135, 45, -15, ...

Therefore, the equation a_n = (-135) * (-3)^(n-1) accurately describes the given sequence.