Fifteen more than twice a number is 9

How many terms are there in the sequence 1, 8, 28, 56, ..., 1 ?

BabaBlast [244]

Answer:

9 terms

Step-by-step explanation:

Given:

1, 8, 28, 56, ..., 1

Required

Determine the number of sequence

To determine the number of sequence, we need to understand how the sequence are generated

The sequence are generated using

$\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}$

Where n = 8 and r = 0,1....8

When r = 0

$\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1$

When r = 1

$\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8$

When r = 2

$\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8$

When r = 3

$\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56$

When r = 4

$\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70$

When r = 5

$\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56$

When r = 6

$\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28$

When r = 7

$\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8$

When r = 8

$\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1$

The full sequence is: 1,8,28,56,70,56,28,8,1

And the number of terms is 9

3 0

3 years ago

Please help me ASAP!!!

brilliants [131]

Answer:

The answer is 100% without a doubt A

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A publishing company is going to have 24,000 books printed. There are between 3 and 4 books out of ever 3,000 that will have a p

vaieri [72.5K]

Answer:

C. 31

Step-by-step explanation:

3000 there are 3-4 errors

If we first divide 24,000 by 3,000, will get 8

then since there a error for each 3,000 books, we do 8 x 4 = 32 and 8 x 3 = 24

32 (8 x 4) the max amount of printing errors

24 (8 x 3) the minimum amount of printing errors

So we should expect 24-32 printing errors

Only answer between the numbers is c. 31

4 0

3 years ago

2 1/8 x+ 3/4 x+ 1/6 − 7/12 x+5 2/3

AleksAgata [21]

Answer:

x = (-28)/11

Step-by-step explanation:

Solve for x:

(55 x)/24 + 35/6 = 0

Put each term in (55 x)/24 + 35/6 over the common denominator 24: (55 x)/24 + 35/6 = (55 x)/24 + 140/24:

(55 x)/24 + 140/24 = 0

(55 x)/24 + 140/24 = (55 x + 140)/24:

(55 x + 140)/24 = 0

Multiply both sides of (55 x + 140)/24 = 0 by 24:

(24 (55 x + 140))/24 = 24×0

(24 (55 x + 140))/24 = 24/24×(55 x + 140) = 55 x + 140:

55 x + 140 = 24×0

0×24 = 0:

55 x + 140 = 0

Subtract 140 from both sides:

55 x + (140 - 140) = -140

140 - 140 = 0:

55 x = -140

Divide both sides of 55 x = -140 by 55:

(55 x)/55 = (-140)/55

55/55 = 1:

x = (-140)/55

The gcd of 140 and 55 is 5, so (-140)/55 = (-(5×28))/(5×11) = 5/5×(-28)/11 = (-28)/11:

Answer: x = (-28)/11

7 0

3 years ago

en una granja quieren poner una cerca con forma octogonal para guardar las ocas por las noches.Ya han colocado dos de los lados

ratelena [41]

Answer:

Perimeter = 32m

Area = 76.8m²

Step-by-step explanation:

Question:

On a farm they want to put an octagonal fence to keep the geese at night. They have already placed two of the sides and used 8 meters of fence. If we know that the apothem is 4.8 meters, what will be its perimeter? And your area?

Octagonal polygon is a polygon with 8sides.

Two sides of fence = 8m

One side of fence = 8/2 = 4m

Each sides = 4m

Apothem = 4.8m

Let's look at the steps that will enable us solve this question.

The area of a regular polygon is calculated as:

Area = ½ap

where a = the apothem of the polygon

p= the perimeter of the polygon.

Apothem is the distance between the centre of the polygon and the base of the polygon.

The perimeter (p) = The sum of all sides of the octagon

p = (4 + 4 + 4 + 4 + 4 + 4+ 4+ 4 )

p = 4(8)

perimeter (p) = 32m

Area = ½ ×a ×p = ½ × 4.8m × 32

Area = 153.6/2

Area = 76.8m²

3 0

3 years ago