#URGENT ARITHMETHIC SEQUENCE PROBLEM

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ionic lilyBOT
lime epoch
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what is arithmetic sequences

dense bronze
lime epoch
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what

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is

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arithmetic

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sequences

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(idk)

dense bronze
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its basically like sequences

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that have a common difference

lime epoch
dense bronze
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or 1,3,5

lime epoch
dense bronze
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or 17,20,23

dense bronze
lime epoch
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okay

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so instead of a, b, c

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you can denote it as

dense bronze
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the difference between a term and the previous term should be the same

lime epoch
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a, a + m, a + 2m

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with a is the smallest number

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and m being the difference

dense bronze
lime epoch
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and you are asking me ohww many arithmetic sequences of positive integers a, b, c that satisfy a < b < c <= 1000

dense bronze
lime epoch
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okay this is combinatorics alr 💀

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add combinatorics please

dense bronze
lime epoch
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so like

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the amount is determined through a and m

polar thorn
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a < a+d < a+2d <= 1000
right noe the firdt methkd that comes to mind:
a = 1:
2d <= 999
d <= 499.5
d takes all positive integers less than, including 499.
Similarly 2:
d <= 499
d takes all positive integrrs less than and including 499
a = 3:
d <= 997/2 = 498.5
You start to realise there's a pattern. Do you see it?

dense bronze
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so then is answer 249500?

lime epoch
polar thorn
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2(499 + 498 + ... + 1) or smt

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Yeah thats that

lime epoch
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basically it

lime epoch
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that's the equation?

polar thorn
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yeah brother

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That comes out to that

lime epoch
dense bronze
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i got the answer by taking d=1,2,3,.......

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and for 1 i got 998, 2 i got 996 so i j continued that to 499

polar thorn
dense bronze
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idk how to prove that this pattern is always the case

polar thorn
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Now take a=2 and so on

dense bronze
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i see pattern

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hence its the answer?

polar thorn
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But since you want integer

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You take floor of the number

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Floor(4.3) = 4
Floor(4) = 4

lime epoch
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(that existed from scratch)

polar thorn
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(Incase you dont know what floor means)

dense bronze
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and why do you multiply

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the whole thing by 2

lime epoch
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floor of it would be 499

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then 499

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498.5

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and blah blah blah

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so that's why you need to multiply by 2

dense bronze
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ohhh

ocean relic
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you can also take a b = half of 1000 = 500

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so a = 499, 488 and so on

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and c goes from 501,502 and so on

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then for (a,c) it can exist as (c,a)

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then for b=499

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so on till b=2

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where a>0

turbid ravine
ocean relic
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but when u shift b to 501 or 502

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c<= 1000

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take this account

polar thorn