Pugzzz
Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

A sequence is shown in the graph.

points at 1 comma 48, 2 comma 12, 3 comma 3, and 4 comma 75 hundredths

Assuming the pattern continues, what is the formula for the nth term?

an = 48(4n)
an = 48(0.25n + 1)
an = 4(48n − 1)
an = 48(0.25n − 1)

A Sequence Is Shown In The Graph Points At 1 Comma 48 2 Comma 12 3 Comma 3 And 4 Comma 75 Hundredths Assuming The Pattern Continues What Is The Formula For The class=

Sagot :

sqdancefan

Answer:

  (d)  48(0.25^(n-1))

Step-by-step explanation:

The points shown on the graph have y-values that decrease by a factor of 4 as x-values increase by 1. The first couple are (1, 48), (2, 12). You want the formula for the n-th term.

Geometric sequence

The terms of a geometric sequence have a common ratio (r). If the first term is a1, the general term is ...

  an = a1(r^(n-1))

Application

The given sequence has first term a1 = 48. The common ratio is ...

  r = 12/48 = 1/4 = 0.25

Using these value in the formula for the general term, we find the n-th term to be ...

  an = 48(0.25^(n-1)) . . . . n-th term of the pattern

[tex]\begin{array}{ccccccccc} 1&&2&&3&&4&&5\\\cline{1-9} \\48&,&12&,&3&,&\underset{0.75}{\frac{3}{4}}&&\underset{0.1875}{\frac{3}{16}}\\[2em]\cline{1-9} &&48\left( \frac{1}{4} \right)&&12\left( \frac{1}{4} \right)&&3\left( \frac{1}{4} \right)&&\frac{3}{4} \end{array}~\hfill \begin{array}{llll} a_1=48\\\\ r=\frac{1}{4} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\stackrel{\textit{first term}}{48}\\ r=\stackrel{\textit{common ratio}}{\frac{1}{4}\to 0.25} \end{cases}\implies a_n=48\left( 0.25 \right)^{n-1}[/tex]

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.