I need help with a sequence

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I need help with a sequence

Mathematics
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10 13 16 8 If i is multiple of 4 divide it by 2 if it is not a multiple of 4 add 3 Find the 500th term The 500th term is 8 but i need a formula to show how i worked it out
10,13,16,8,11,14,17,20,10,13,16,8 Then we can see that \(a_4=a_{12}=8\) and in general \(8=a_4=a_{4+8n}\) for any \(n\). Since \(500=4+8n\Leftrightarrow 496=8n\Leftrightarrow n=124 \) then \(a_{500}=8\).
1. 8+3=11 2. 11+3=14 3. 14+3=17 4. 17+3=20 5. 20/2=10 6. 13 7. 16 8. 8 this will be repeating now the 4th element is 8 plus every 4+k8 element (k is an integer) 500=4+62*8 so it is 8

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Other answers:

Andras is right for the \(n\) :).
The rule is if it is a multiple of 4 divide it by 2 so 8/2 =4/2=2+3=5+3=8/2=4/2=2+3=5
that is what keeps on happening
haha watchmath we both suck :)
10 13 16 8 below four will be repeating than 4 2 5 8 so we can see that every 4th element is 8. 500/4=125 this proves that it is 8
but 500 also divides by 4 so how can u be certain that it is 8
every 4th element is an 8 (we can see that now) so if an element can be written as the the factor of 4 than it is 8. 1*4th element=8 2*4th =8 3*4th =8 and so on so the 125*4th element (500)=8
ok thank you very much for helping me
no prob
What is the formula
I dont think there is a formula here, you have to use your brain
Are you sure because my dad says there is a formula but will not tell me
the formula us that if the number can be written as 4k (k is an integer) than it is 8, I dont see what your dad wants.
ok thanks i will go now and prove my dad wrong
Good luck for that! :-)
Well you can make a formula \(a_1=10,a_2=13,a_3=16\) \(a_{4n}=8\) for all \(n\) \(a_{4n+1}=4\) for \(n\geq 1\) \(a_{4n+2}=2\) for \(n\geq 1\) \(a_{4n+3}=5\) for \(n\geq 1\)
can you make the formula for me pretty please
I wrote the formula above! You need to free your mind! the formula doesn't always means that you have to write it as a single expression. The description above is count as formula too.
ok i need to tell you something i am an 11 year old child in harrow that goes to Glebe Primary School my teacher gave me a sequnce and i had to find out the 500th term usin a simple formula do u think i can understand wat u just wrote
at 11 you learn about sequences?? tell your teacher to relax a bit :-)
i have to find a formula to be in this level six study group at school
Ok, you must be smart since your teacher has a high hope for your and give you this problem. The formula that I gave above basically says that to find the nth terms of the sequence (were \(n\geq 4\) )) we do the following: When n/4 has no remainder, then the nth term is 8 when n/4 has 1 as the remainder, then the nth term is 4 when n/4 has 2 as the remainder, then the nth term is 2 when n/4 has 3 as the remainder, then then nth term is 5 For example what is the 6666th term? Lets divide 6666/4. We have 1666 with remainder 2. So the 6666th term is 2.
ooooooooooooo i get it
so 500/4 is 125 with no remainder so it is 8
perfect!!
thank u very much u are the best u should get a job as a teacher
wat do u mean by remainder 6666/4=1666.5 so how is it 2
\(6666=4\cdot 1666 + 2\) So the remainder is 2. You need to divide by hand to get the remainder.
what is the hand
By hand means not using calculator. No body teach to divide by "hand" anymore? :D
how does 6666= 4.1666+2=
i hav no idea where u get the remainder 2 from
Do you know how to divide just using paper and pencil?
yes i do
Ok, try to divide 6666 by 4 using paper and pencil.
ooooooo i see it now thank u very much u are the best
good for you :D
bye thank u so much

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