Question

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)

Answer 1

`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}}{(1)/(4)\to 0.25} \end{cases}\implies a_n=48\left( 0.25 \right)^(n-1)`

Answer 2

(d) 48(0.25^(n-1))

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