Question

Which of the following choices is the explicit formula for the following

geometric sequence?
-0.1, 0.04,-0.016, 0.0064,-0.00256

Answer 1

Step 1 :

In question, we are asked to find the explicit formula of the Geometric Sequence.

Considering the Geometric Sequence,

- 0. 1 , 0. 04 , - 0.016 , 0.0064, -0.00256, ............

Step 2 :

We have that First Term, a = - 0. 1

`\text{Common Ratio, r = }\frac{T_2}{T_1\text{ }}\text{ = }\frac{0.04}{-0.\text{ 1}}\text{ = - 0. 4}`

Step 3 :

Using the nth term of the Geometric Sequence,

`\begin{gathered} T_{n\text{ }}=ar^(n-1) \\ \text{When a = -0. 1} \\ r\text{ = -0. 4} \end{gathered}`
`T_n=(-0.1)(-0.4)^{n\text{ - 1}}\text{ -- OPTION E}`