Stteps for solving 6(4x-3) are shown<br><br> which of these is not a part of the solution prosess

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

Nick can type 30 words a minute.<br> How many words can be typed in 9.5 minutes?

iren [92.7K]

Answer:

285 Words

Step-by-step explanation:

If in 1 minute he can type 30 words , then in 9.5 min he can type 30 x 9.5 = 285.0 = 285

So, Nick can type 285 words in 9.5 minutes.

Hope this Helps!

7 0

3 years ago

Which number is a prime 49 51 53 55

shtirl [24]

53 is a prime number !!

3 0

3 years ago

Read 2 more answers

Which inequality represents all possible solutions of -12d2 -6?

qaws [65]

Answer:

f

Step-by-step explanation:

6 0

3 years ago

Sylvia has a piece of material that is 668.36 square inches. She marked the material into 4 equal pieces and then cut out one of

sveta [45]

The whole magic jug had 668.36 ounces of mysterious elixir in it.
Sylvia came along and marked it into 4 equal amounts, so each
amount was (1/4) of (668.36 ounces).

Now, you would have us believe, she tucked the magic jug under her cloak,
walked quickly and quietly down the hall into the shadows, pulled the jug out,
and quaffed one of the equal amounts from it, all in one slug.

The quantity remaining in the jug was then

(3/4) of (668.36 ounces) = 501.27 ounces.

The same process works for length, volume, area, stones, money, anything.
If you divide up what you have into 4 equal parts, then each part is 1/4 .
If you eat, sell, lose, or give away 1/4 of it, you have 3/4 left.

8 0

3 years ago

Read 2 more answers

Stteps for solving 6(4x-3) are shown which of these is not a part of the solution prosess