Which choice is the explicit formula for the following geometric sequence?

Question

0.3, -0.06, 0.012, -0.0024, 0.00048

A. a_n = -0.3(0.2)^(n-1)

^B. a_n = -2.0(0.3)^(n-1)

C. a_n = -0.3(-0.2)^(n-1)

D. a_n = 0.3(-0.2)^(n-1)

E.a_n = 0.3(0.2)ⁿ

Answer 1

Hi Emma

The answer here is D.

The first thing to notice is the first number in the sequence - your initial value of 0.3.

The second clue is the numbers alternate between positive and negative so the (-0.2).

Third, the exponent should be n-1. I'll try to explain this in a moment.

Putting the above together, start with the initial value 0.3 times the negative (-0.2) with the exponent^(n-1)_.

or 0.3(-0.2)^(n-1)

Let's take a closer look.

a₁ =.03(-0.2)⁰ = 0.3 If we start with n=1 (1 representing the first number in the sequence), by using n-1 (1-1=0), we get an exponent of 0, which is the same as multiplying times 1. Anything raised to the power 0 =1. So a₁ =.03(-0.2)⁰ becomes 0.3(1) which gives us the first/starting number.

Each time n is an even number, n-1 will be an odd number. Any negative number raised to a odd power gives a negative result and raised to an even power gives a positive result. So we have alternating positive and negative values.

a₁ =.03(-0.2)⁰ = 0.3

a₂ =.03(-0.2)¹ gives us 0.3(-0.2) or -0.06.

a₃ =.03(-0.2)² gives us 0.3(0.04) or 0.012.

a₄ =.03(-0.2)³ gives us 0.3(-0.008) or -0.0024.

a₅ =.03(-0.2)⁴ gives us 0.3(0.0016) or 0.00048.