Answered

From simple questions to complex issues, IDNLearn.com has the answers you need. Get accurate and comprehensive answers from our network of experienced professionals.

Which choice is the explicit formula for the following geometric sequence?0.5, -0.1, 0.02, -0.004, 0.0008, ...O A. an = -0.5(0,2)(n-1)B. an = 0.5(0.2)"C. an = 0.5(-0.2)(n-1)D. an = -0.5(0.3)(n-1)E. an = -0.5(-0.2) (n = 1)N

Sagot :

The nth term of a geomeric series having first term 'a' and the common ratio 'r' is given by,

[tex]a_n=a\cdot r^{n-1}[/tex]

Now, consider the given geometric sequence,

[tex]0.5,-0.1,0.02,-0.004,0.0008,\ldots\ldots[/tex]

Observe that the first term of the sequence is 0.5,

[tex]a=0.5[/tex]

The common difference is calculated as,

[tex]\begin{gathered} r=\frac{a_2}{a_{}} \\ r=\frac{-0.1}{0.5} \\ r=-0.2 \end{gathered}[/tex]

Substitute the values,

[tex]a_n=(0.5)(-0.2)^{n-1}[/tex]

This expression is given in option C. Therefore, option C is the correct choice.

We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.