We appreciate your visit to Which recursive formula can be used to define this sequence for tex n textgreater 1 tex tex 44 11 frac 11 4 frac 11 16. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We begin by writing the sequence:
[tex]$$
a_1 = 44,\quad a_2 = -11,\quad a_3 = \frac{11}{4},\quad a_4 = -\frac{11}{16},\quad \ldots
$$[/tex]
Step 1: Calculate the ratio between the second term and the first term:
[tex]$$
\text{ratio} = \frac{a_2}{a_1} = \frac{-11}{44} = -\frac{1}{4}.
$$[/tex]
Step 2: Verify that this common ratio is consistent by computing the third term:
[tex]$$
a_3 = a_2 \times \left(-\frac{1}{4}\right) = -11 \times \left(-\frac{1}{4}\right) = \frac{11}{4}.
$$[/tex]
Since the ratio remains [tex]$-\frac{1}{4}$[/tex] from term to term, the sequence is geometric.
Step 3: Therefore, the recursive formula for the sequence is:
[tex]$$
f(n) = -\frac{1}{4} \, f(n-1) \quad \text{for } n > 1.
$$[/tex]
Among the options provided, this corresponds to the third option.
[tex]$$
a_1 = 44,\quad a_2 = -11,\quad a_3 = \frac{11}{4},\quad a_4 = -\frac{11}{16},\quad \ldots
$$[/tex]
Step 1: Calculate the ratio between the second term and the first term:
[tex]$$
\text{ratio} = \frac{a_2}{a_1} = \frac{-11}{44} = -\frac{1}{4}.
$$[/tex]
Step 2: Verify that this common ratio is consistent by computing the third term:
[tex]$$
a_3 = a_2 \times \left(-\frac{1}{4}\right) = -11 \times \left(-\frac{1}{4}\right) = \frac{11}{4}.
$$[/tex]
Since the ratio remains [tex]$-\frac{1}{4}$[/tex] from term to term, the sequence is geometric.
Step 3: Therefore, the recursive formula for the sequence is:
[tex]$$
f(n) = -\frac{1}{4} \, f(n-1) \quad \text{for } n > 1.
$$[/tex]
Among the options provided, this corresponds to the third option.
Thanks for taking the time to read Which recursive formula can be used to define this sequence for tex n textgreater 1 tex tex 44 11 frac 11 4 frac 11 16. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
