Which answer describes the type of sequence?

Mathematics

1 answer:

jeyben [28]3 years ago

6 0

Answer:

The sequence is a geometric sequence.

Step-by-step explanation:

The given sequence is

$\frac{1}{6},\frac{1}{2},\frac{3}{2},\frac{9}{2},...$

We examine to see whether there is a common difference or a common ratio.

We first check for a common difference by subtracting the subsequent terms.

$\frac{1}{2}-\frac{1}{6}=\frac{2}{3}$

$\frac{3}{2}-\frac{1}{2}=1$

The two differences are not equal.

Hence the sequence is not arithmetic.

We now look out for a common ratio.

$\frac{1}{2}\div \frac{1}{6}=3$

$\frac{3}{2}\div \frac{1}{2}=3$

$\frac{9}{2}\div \frac{3}{2}=3$

Since there is a common ratio of 3, the sequence is geometric.

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HELP!! PLEASE A carpenter is framing a window with wood trim where the length of the window is 9 and 1/3 feet. If the width of t

ohaa [14]

We need the perimeter of the window for framing

The window is in the shape of a rectangle with the height of $9 \frac{1}{3}$ feet and width of $6 \frac{3}{4}$ . The diagram of the shape is shown below

The perimeter of a shape is obtained by adding up the length of all the sides that form the shape.

The perimeter of the window is $9 \frac{1}{3}+9 \frac{1}{3}+6 \frac{3}{4}+6 \frac{3}{4}$ = $18 \frac{2}{3}+12 \frac{6}{4}$

We have two whole numbers 18 and 12 and two fractions $\frac{2}{3}$ and $\frac{6}{4}$

Adding the two fractions that have different denominator
$\frac{2}{3}+ \frac{6}{4} = \frac{8}{12}+ \frac{18}{12}= \frac{26}{12}$ , which is an improper fraction which we can change into a mixed number $2 \frac{1}{6}$

So the perimeter of the window is
$18+12+2 \frac{1}{6} =32 \frac{1}{6}$

and the length of wood needed for the frame is $32 \frac{1}{6}$ feet