Question

Hi guys, I need help with a sequence problem :

Find the next term in this sequence :
24,54,90,120,168,210,240,288,360,440

I've been trying this for quite some time now and I'm not getting the logic. Help is solicited. Thanks in advance!

Answer 1

Hello Welcome to OpenStudy!

Can you tell which part you are stuck at exactly so I can help you. Thank you. :)

Answer 2

30
36
30
48
42
30
48
72
80

Those would be the changes in between each of the numbers. Does that clear it up a little? Are there any options for this question? @ripazha

Answer 3

thanks for the reply! i am trying to find the pattern here. I calculated the term differences. That turned out to be non-constructive.
I don't know what to do after that

Answer 4

\(\rlap{\color{red}{\huge\bigstar}\huge \color{green}{ \text{Welcome to Open Study! }}\color{red}\bigstar}{\; \color{aqua}{\huge\bigstar}\huge \color{aqua}{\text{Welcome to Open Study! }}\color{yellow}\bigstar}\) @ripazha

Answer 5

I don't see the pattern from the differences. can you elaborate? thanks

Answer 6

all of your numbers are divisible by 6, except the last, namely 440

Answer 7

if there's no pattern in differences, then the sequence is not a polynomial sequence..

Answer 8

@hartnn , so? What should I do after that?

Answer 9

Are you learning about Cubed numbers? Or squared numbers? Or Triangular number? Or Geometric sequences?

Answer 10

this was in one of the iq tests at school

Answer 11

is it 990?

Answer 12

To find a missing number, we need the rule. Is there something that I missed? Or is there no rule yet?

Answer 13

we need to find that rule/pattern joel

Answer 14

@MARC_ How?

Answer 15

any choices are given ?

Answer 16

FOUND IT!
I think..
It ha only worked with 2 of them so far give me a sec...

Answer 17

@Michele_Laino , How?

Answer 18

24 = 6 * 4
54 = 6 * 9
90 = 6 * 15
120 = 6 * 20
168 = 6 * 28
210 = 6 * 35
240 = 6 * 40
288 = 6 * 48
360 = 6 * 60
440 = 6 * 73.33

i guess the question is wrong...

Answer 19

It should be around 520

Answer 20

ganpat, but there is no pattern in 4,9,15,20....is it ?

Answer 21

hmm ever mind I thought of it wrong...

Answer 22

Guys, I appreciate your help but it would really help if you mention the logic

Answer 23

\(2^3 . 3\)
\(2 .3^2\)
\(2 . 3^2.5\)
\(2^3. 3.5\)
\(2^3. 3.7\)
\(2 . 3.5.7\)
\(2^2. 3.5.7\)
\(2^5. 3^2 \)
\(2^3. 3^2.5\)
\(3^2. 5.11\)

Answer 24

@hartnn : right.. so i feel the question is wrong or may some values are wrongly written.

Answer 25

so since 3 every where lets see what we got

Answer 26

Ok first off before we jump to an answer., It would be nice to know what you learning about. Are you in geometry or algebra, or what?

Answer 27

@Ganpat question is right. my teacher was confident and he has a solution which he won't reveal

Answer 28

wait i have typo

Answer 29

\(2^3 . 3\)
\(2 .3^2\)
\(2 . 3^2.5\)
\(2^3. 3.5\)
\(2^3. 3.7\)
\(2 . 3.5.7\)
\(2^2. 3.5.7\)
\(2^5. 3^2 \)
\(2^3. 3^2.5\)
\(2^3. 5.11\)

Answer 30

one more
2nd line
\(2.3^3\)

Answer 31

so 2 every where not 3 :P

Answer 32

\(2^3 . 3\)
\(2 .3^3\)
\(2 . 3^2.5\)
\(2^3. 3.5\)
\(2^3. 3.7\)
\(2 . 3.5.7\)
\(2^2. 3.5.7\)
\(2^5. 3^2 \)
\(2^3. 3^2.5\)
\(2^3. 5.11\)

now fine ?

Answer 33

since your sequence is:
24=6*4
54=6*9
90=6*15
....
360=6*60
now 440 is not divisible by 6, nevertheless if we note that:
440=110*4
now I start a sequence as above, with 110 in plce of 6 namely the next term is:
990=110 *9

Answer 34

@ripazha : ha haa.. No offenses.. just a second thought :p

Rule of Mathematics: If you can`t prove it right, then prove it wrong :D

Answer 35

oops ...in place of...

Answer 36

I give up... whoever solves this is a genius

Answer 37

@Michele_Laino , according to your argument, where did 440 come from? Your argument doesn't explain the presence of 440

Answer 38

can u post a screenshot of question

Answer 39

@mathmath333 ,why?

Answer 40

i will put that in a supercomputer

Answer 41

kidding , just want to know if anything is incorrect or misspelled

Answer 42

@mathmath333 I'm 100 % sure that the question is right. I've checked a dozen times

Answer 43

cuz yesterday o guy posted \(9\) as \(g\)

Answer 44

I thought that was an arbitrary change in your sequence @ripazha

Answer 45

@Michele_Laino I don't think so. @mathmath333 again. I'm 100% sure about the question

Answer 46

yes , but thats the only chance if any i think

Answer 47

@mathmath333 ?

Answer 48

i got weird pattern

Answer 49

for now even weird is good enough to consider :P

Answer 50

Ok - I have plotted these numbers. their differences and their sin

It ia fairly evident that there is no arithmetic, geometric or trig relationship between them.

You said that this came from an IQ test. Now it is my experience that IQ tests are not always mathematically related, and sometimes require a you to spot a relationship other than purely mathematical.

Right now I don't see a pattern - but I think we may be looking in the wrong place if we pursue a rigourous mathematical approach.

Nice question...

Answer 51

i guess we need to think out of the box!

Answer 52

n x(n) div by 2 x(n)/2 - x(n-1)/2 x(n)/2 mod x(n-1)/2
1 24 12 Null Null
2 54 27 15 3 or 15
3 90 45 18 18
4 120 60 15 15
5 168 84 24 24
6 210 105 21 21
7 240 120 15 15
8 288 144 24 24
9 360 180 36 36
10 440 220 40 40

Answer 53

so nw we can find something :D

Answer 54

lets try it :-
x(1)=2*12
lets find x(2)

x(2)/2-12=x(2)/2 mod 12
so
x(2)/2=27
x(2)=54

Answer 55

which is something silly and i just note it wrong >.<

Answer 56

lol

Answer 57

is it a number close to 450?

Answer 58

@Michele_Laino , as i've mentioned before, I don't know the answer. If you give the logic, it'd be great

Answer 59

@ripazha
Perhaps it is NOT logic.

Look at the numbers, maybe there is a link to non-sequential items.

scores in games? number of days between moonshots, number of months each Pope lived ..... blah blah - all I'm saying is that for IQ tests you cannot rely on maths - you may need to be more creative.

Answer 60

@MrNood , I don't think so. My teacher said there is A solution.

Answer 61

ok!
I write your sequence:
6*4-6*9-6*15-6*20-6*28-6*35-6*40-6*48-6*60-440
now (4+15)/2-1=9, so the mid term between 24 and 60, is 6*9=54,
at the same way, if I suppose 444=6*74 instead of 440, I have:
(48+74)/2-1=60, so the mid term between 288 and 440 is 6*60=360.
Again for the next term, namely y=6*x we have:
(x+60)/2-1=74, from which x=90, so the next term to 444 is 6*90=450.

Answer 62

and that reasoning would explain the presence of 440

Answer 63

@ganeshie8

Answer 64

it is nto there in oeis and wolfram also gave up so im not so sure.. id like to know the source of this problem / level of difficulty before attempting

Answer 65

it is school level iq test so it should be simpler than mods and congruences stuff hmm

Answer 66

i know it should be clear observation , but see not linear relation neither cubic or quadratic , was thinking it should be something without calculating like digits replacement

Answer 67

yeah im trying interleaving sequences and other non-math related things

it cannot be a polynomial because the differences are not converging and also it cannot be an exponential because the differences keep increasign and decreasign

Answer 68

i agree

Answer 69

no success :O
il wait for the teacher to show how to solve i guess :)

Answer 70

Hey guys, I called my teacher to ask about this, and he said ; Do whatever you want. I just want a closed form solution. You are free to use any operations.