#generating sequence

[alwaysmathematics]

Sequences and functions

Generating sequences

A sequence is an ordered set of numbers/ terms arranged according to a specific rule. For example : 3, 7, 11, 15, 19. This sequence has 5 terms, in order according to a specific rule, added by 4.

There are two types of sequence:

Linear Sequence : each term will be increased or decreased by the same number. For example : 5.3, 4.5, 3.7

Non-Linear Sequence : each term will be increased or decreased by a different number. For example : 2, 4, 8, 16

Finding the nth term

You can find the value of a term based on its position. It is called as an nth term. The value of n is the position of the term. Here is the general way to construct the nth term of 3, 7, 11, 15, 19.

find the rule of the sequence

multiply it with the value of n

find the value of term before term position 1

place the result of step no 3 next to the result of step no 2

Now, we will execute them. (1) the rule of the sequence is "added by 4". (2) multiply it with the value of n, 4n. (3) find the value available before term position 1 is 3 - 4. The result is -1. (4) place the result of step no 3 next to the result of step no 2, 4n - 1. So the nth term of 3, 7, 11, 15, 19 is nth= 4n - 1

With this nth term, we can find the value of term in any position! For example, we want to know the value of term position 121 of the above sequence, 3, 7, 11, 15, 19. It means the value of n is 121. The nth term of this sequence is 4n - 1. Substitute the n with 121. It becomes nth term = (4 x 121) - 1. The result is 483. The value of term position 121 for this sequence is 483.

What will be nth term of 5.3, 4.5, 3.7? and find the value of term position 98. The answer of this question will given at the end of the post.

Finding the inverse of a function

Function can be in 3 different forms, an equation, a mapping and an function mapping. When you give an input to a function, you will get an output.

The example of function in the form of an equation is y = 3x - 2. From this equation, we can say " to get the value of y, we need to multiply the value of x by 3 and minus it by 2". The conclusion, x is the required input so that the function or the calculation can be executed in order to get the output, y.

The look of the mapping form for the same function is x → 3x - 2. The most left, x, is the input. The next one is the process should be done to the value of x (function) in order to get the output, y.

Above is the example of a function machine. X is the input to the function. The function will multiply the value of x by 3 and minus it by 2. The result of the function becomes the value of y. Y is the output.

The process or the function is read from left to right. When we read it in the opposite way, we can called it as inverse of the function. Here are the steps for inversing a function.

change the x to y and y to x

use the left arrow instead of right arrow

change the operation to the opposite one , minus to plus, plus to minus, multiply to divide, divide to multiply, square to square root, square root to square

Here is the result of inversing the function using a function machine.

The result of inverse the function :

in the form of equation is y = (x + 2)/3

in the form of mapping is x → (x + 2)/3

Work out the inverse function for y = (x + 1)/2. The answer of this question will given at the end of the post.

NOTE: When I want to find the inverse of the function, if it is possible, I will use a function machine. This question looks simple but if you don't understand well the function is and you don't know very well about the order of operations, you might make a mistake for this question.

The answer for:

What will be nth term of 5.3, 4.5, 3.7? nth = -0.8n + 6.1

find the value of term position 98. (-0.8 x 98) + 6.1 = -72.3

The inverse function for y = (x + 1)/2. y = 2x - 1

Thank you.

[horzagobuchul]

Yours truly needs to eat too, you know!

[luck-of-the-drawings]

THIS THING IS SCUUUFFED AS HELL & ITS ALSO THE BEST THING I HAVE ANIMATED THUS FAR. IM SO IN LOVE WITH EMIZEL. JUST WISH I GAVE HIM MORE STUPID TATTOOS. NEXT TIME THO. NEXT TIME. I ALSO LOVE VEX&VIV SOOOO MUCH. charlies flavor of Deranged is my FAVORITE!!

[the-heart-of-a-monster]

THOAM ISSUE 7 PAGE 32

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[lastoneout]

Magical girl transformations are literally never not hype. I’m never sick of them, idk how many times I see them or how much episode time they take up or if they make any sense at all they are always awesome. I don’t even have to give a shit about the characters or the show I see a magical girl transformation and my brain just goes

[incadigitalart]

Here’s some more Ellie for you ❤️

I’m looking to change my tumblr name. What do you think? Let me know below!

[itsmissing]

that one scene from Let's Go Kamen Riders that's basically cocomelon for early rider fans

[july-19th-club]

seven or eight times now ive watched the episodes in which they take the andromache and this is the first time ive realized that during the initial battle, after they board, every time the camera is from dufresne's perspective it's blurrier than otherwise because. he took his glasses off for the fight

[iwonderwh0]

No, but if Hank chose the wrong Connor, he won't live long after the fact – the guilt will be too heavy to bear

[horzagobuchul]

Lara Croft, pastry raider~

[madamescarlette]

Also in the current cinema environment that is very much oriented towards filmmakers who love to shine the light on the act of filmmaking, it's weirdly such a comfort to see The Fall Guy is made by someone who loves movies themselves!

[stone-stars]

i'm going to sue murph for emotional distress over the valiant ol' cobb being used when marabelle is defeated and the gunslinger's girl being used in the flashback to what happened the day she was tricked. jesus christ.

[un-pearable]

i think ninjago fans need to rewatch s3e7 every once in a while. to keep them humble and remind them of the wonders of an early 2010s lego that didn’t give a shit

[ymofan04]

Roland SH-101

[snaplight-anxiety]

Okay so here’s my piece on the lighting in alex rider

Alright. So s1e7 happens, you think everything went well and it’s all wrapped up. But at the end of it, they shows alex still in the school, looking roughed up and we realize that he ALSO had a clone (which, though hinted at through the episodes, I at least had forgotten about bc come on! everything is good now!) and you realize that you can’t tell, of the two (one left at the school, one taken home) who is the clone and who is the original.

What I found really fascinating was how they portrayed the two to play up that confusion. The one left at the school is consistently shown in well lit scenes. I'm pretty sure he’s always in bright lighting or at least with no obvious shadows. In the sequence where he goes from the rubble to the study, inside the school itself, there aren’t any ominous shadows or shots that stand out to me. Instead, there are big windows with lots of light from outside. It just feels eerie in the fact that he’s alone and all the evil inhabitants are gone (presumably). When he gets outside, he wears a bright yellow coat and the snow is bright white and makes the scenes themselves even lighter.

On the other hand, the Alex they brought home is shown consistently in darkness. In e7, he looks at the helicopter that comes to save them with a blank, confused and almost cynical look. When he gets back home Jack and Tom are there to greet him, but he ignores them, goes to his room, and closes the door in their faces. He is consistently facing away from the camera, or his face is entirely in shadow so you can’t see his expression.

It makes my brain go a little wild and I think it was a pretty ingenious thing to do, because one, if there hadn’t been a clone, it would be a pretty smart and realistic way to convey the idea of Alex coming home and not being able reconcile his old life and what he’s lived through bc they’re so conflicting and he has trauma and it’s like this veil has been lifted; everything about him is different but everyone expects him to go back to normal and he can’t.

But because there is a clone, because of the double that was left behind, those lighting choices cast doubt over whether or not that’s the real Alex. Is he acting closed off and different because he’s a different person metaphorically or literally?

Especially because we know the clones are evil, the choice to put one in darkness and not show his face and the other in bright scenes and colors (along with the scene where Tom informs Alex about the dance and the fact that generally the clone plot twist implies that the character you’ve mostly been watching isn’t who you thought he was), it adds up to making you think they got switched and Alex (good guy, well lit) has been left behind. The clone (dark, shadowy, motive unclear) has been taken in in his place.

But then you see the one who was left behind bash someone on the head with a rock and steal his car (still in the brightly lit shots) and you realize that you really cannot tell who is who. Because the storytelling of the lighting and shot angles is telling you one thing, but the actions are telling you something completely different. It forces you to confront the idea that maybe you didn’t really know Alex at all and maybe he always had that in him, because the one in England is obviously the evil one right? But Alex is the protagonist, he couldn’t have done that. And yet….

I go wild for the use of lighting as a physical plot device, because it isn’t really something I’ve seen before. Usually lighting in film (from what I’ve seen) only implies things about characters (dark=evil, unclear faces=hiding thoughts) or places (not well lit=bad things will happen/jumpscares/hiding things from the audience and characters) the way the music does. It’s all in the background. It isn’t particularly noticeable, because it generally fits with the direction the atory is taking. But the way it is used here as a purposeful misdirection is fascinating. Somebody thought we could use this and they did and it paid off. It’s a very masterful way to take advantage of the type of media they’re using to convey the story. Actually, I think that’s really it. It’s a brilliant adaptation of book to tv, because it conveys the same confusion in a new format in ways you don’t usually see in book adaptations.

Usually adaptations have trouble going from words to a screen because they’re two separate kinds of media and very different ways to communicate. They’re basically two separate languages. A lot of times, trying to get the book’s message through to film doesn’t work out because in books, you can read the actual thoughts and feelings of the characters. On tv, you have to figure out a way to convey that through pictures and dialogue. And this segment specifically of the alex rider show did it brilliantly, because they saw the options at their disposal and figured out a way to translate writing to film with specific components of film that make it make sense in a visual context.

[incadigitalart]

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#SummertimeBonanza