I need help with a sequence

- anonymous

I need help with a sequence

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- anonymous

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

- watchmath

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 \(a_{500}=8\).

- anonymous

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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## More answers

- watchmath

Andras is right for the \(n\) :).

- anonymous

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

- anonymous

that is what keeps on happening

- anonymous

haha watchmath we both suck :)

- anonymous

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

- anonymous

but 500 also divides by 4 so how can u be certain that it is 8

- anonymous

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

- anonymous

ok thank you very much for helping me

- anonymous

no prob

- anonymous

What is the formula

- anonymous

I dont think there is a formula here, you have to use your brain

- anonymous

Are you sure because my dad says there is a formula but will not tell me

- anonymous

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.

- anonymous

ok thanks i will go now and prove my dad wrong

- anonymous

Good luck for that! :-)

- watchmath

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 \(n\geq 1\)

- anonymous

can you make the formula for me pretty please

- watchmath

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.

- anonymous

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

- anonymous

at 11 you learn about sequences?? tell your teacher to relax a bit :-)

- anonymous

i have to find a formula to be in this level six study group at school

- watchmath

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.

- anonymous

ooooooooooooo i get it

- anonymous

so 500/4 is 125 with no remainder so it is 8

- watchmath

perfect!!

- anonymous

thank u very much u are the best u should get a job as a teacher

- anonymous

wat do u mean by remainder 6666/4=1666.5 so how is it 2

- watchmath

\(6666=4\cdot 1666 + 2\)
So the remainder is 2.
You need to divide by hand to get the remainder.

- anonymous

what is the hand

- watchmath

By hand means not using calculator. No body teach to divide by "hand" anymore? :D

- anonymous

how does 6666=
4.1666+2=

- anonymous

i hav no idea where u get the remainder 2 from

- watchmath

Do you know how to divide just using paper and pencil?

- anonymous

yes i do

- watchmath

Ok, try to divide 6666 by 4 using paper and pencil.

- anonymous

ooooooo i see it now thank u very much u are the best

- watchmath

good for you :D

- anonymous

bye thank u so much

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