#generating sequence

[vardapilled]

Interviewer: "What was like the toughest day on set, would you say?" Ryan (to MBJ): "Twin day. Your last twin day. The cigarette pass. [It was] 120 [degrees], I think." Michael: "Yeah, that was intense. Multiple takes, not a lot of movement so you're standing still in the heat."

MICHAEL B. JORDAN as THE SMOKESTACK TWINS -> Behind the Scenes Composite Shot Featurette Sinners (2025) dir. Ryan Coogler

[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.

[egophiliac]

A-anime?

you know, sometimes I forget that Twst is actually an isekai that starts with the protagonist getting run over by an inexplicable horse-drawn carriage. and every time I'm reminded is a delight because that's AMAZING.

also. look. okay. there's a lot of very fun stuff in the trailer but I am obsessed with that Crowley surprised pikachu face. me when I spend all my keys and gems literally hours before they announce overblot SSRs and drop the anime trailer:

[novelconcepts]

Such a testament to Hahn’s skill as a comedy performer, that as unhinged as the episode one interrogation read from her side, seeing it from Billy’s perspective is just fucking bananas.

[sparkles-rule-4eva]

That... was possibly the most intense nightmare sequence I have ever seen.

The way it started out innocent, sweet, making us think it was just a memory, or a scene being shown from Shadow's past.

The way the fight between Shadow and Gemerl ensued, only to quite literally shatter as Shadow punched him and found himself instead punching glass and winding up somewhere else entirely.

How he was putting the events together in such a way that made us realize - this is a nightmare. This is just one of many times he's relived that day. 😭

The haunting atmosphere of him landing in the prison cell where Gerald sat silently, eyes aglow as the lamp above him swung back and forth so eerily.

...only to glitch away from him again and again when he tried to warn the professor that they needed to leave.

The way he was floating in the red space, looking oh so small and scared with how far away the perspective is.

And those cruel flashes of Maria, terrified and calling for him. 😭

"Shadow! Remember!"

and he wakes up in such a violent panic that he immediately summons a Chaos emerald and blasts the nearest tree to bits.

I just... this felt like a deeper dive into his trauma, his PTSD, that hasn't been shown enough before. He did mention that it "wasn't an ordinary nightmare," but still. That was... that was insane.

Not to mention all the flashes and glitches, that would catch him so off guard during the nightmare, uggghhhh. Someone get this boy to therapy. 😭😭🖤❤️

[sforzesco]

serbisyo / "ginto" / utang (na loob)

As for his literary pursuits, [Crassus] cultivated chiefly the art of speaking which was of general service, and after making himself one of the most power­ful speakers at Rome, his care and application enabled him to surpass those who were most gifted by nature. For there was no case, they say, however trifling and even contemptible it might be, which he undertook without preparation, but often, when Pompey and Caesar and Cicero were unwilling to plead, he would perform all the duties of an advocate. And on this account he became more popular than they, being esteemed a careful man, and one who was so ready with his help.

Plutarch, Crassus

[syringaledraws]

Upwards, onwards

[lesbian-david-tennant]

I just watched Star Trek: The Motion Picture and wow that really is some gay shit

I'd seen the "this simple feeling" scene, I was prepared for that. but I wasn't prepared for the full extent of the conversion therapy allegory

and then Spock saying "it knows only that it needs but like so many of us, it does not know what" while gazing at Kirk

and then the whole fucking resolution being that V'ger needs to discover something more, "a human quality, our capacity to leap beyond logic," through union with a human

it clearly parallels Spock and Kirk with V'ger and Will and directly implies that 'this simple feeling' is love, romantic love

WHAT THE FUCK I can only begin to understand what my fandom ancestors felt seeing this in 1979

[baejax-the-great]

If I were a writer at a big game company working on a sequel to a beloved series and the higher ups kept telling me to make the game shittier and kept sending my work back to me to be dumbed down even further somehow, and then once most of the writing was done they laid me and my coworkers off illegally without severance, I'd probably gleefully watch as people trashed the shitty game that shipped.

[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!!

[tears-of-xion]

I wanna see them dance together! 💖

(close up underneath the 'read more'!)

-

Please do not use or re-post/re-upload my artwork without my permission. Thank you!   (reblogs, however, are welcome and appreciated)

I do not own Hazbin Hotel, nor it’s characters. All rights to their owners.

[dreamsequencermusic]

do not ride alone

[lemonlimestar]

i simply think that it is beautiful that kon both wears his heart on his sleeve and also keeps his innermost secrets deep inside & would rather make himself sick over them than put the burden on someone else 🔥he can agonize over superman not telling him he has a secret identity, or tim not revealing his real name, and be relatively upfront and candid on how he feels but do nottt make him think about his suicidal tendencies or he’ll—well.

[hillclan-ruins]

Moon 11, part 3:

Frostswirl goes for a nice long walk with Scalestar. She confesses her feelings to Scalestar, asking to be mates. And the answer, well, it's not yes. She fell from a cliff and somehow survived, though not without breaking her leg.

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[the-heart-of-a-monster]

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