Question

I need help with a sequence

Answer 1

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

Answer 2

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 \(a_{500}=8\).

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

that is what keeps on happening

Answer 7

haha watchmath we both suck :)

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

ok thank you very much for helping me

Answer 12

no prob

Answer 13

What is the formula

Answer 14

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

Answer 15

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

Answer 16

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.

Answer 17

ok thanks i will go now and prove my dad wrong

Answer 18

Good luck for that! :-)

Answer 19

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 \(n\geq 1\)

Answer 20

can you make the formula for me pretty please

Answer 21

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.

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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.

Answer 26

ooooooooooooo i get it

Answer 27

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

Answer 28

perfect!!

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

what is the hand

Answer 33

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

Answer 34

how does 6666=
4.1666+2=

Answer 35

i hav no idea where u get the remainder 2 from

Answer 36

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

Answer 37

yes i do

Answer 38

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

Answer 39

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

Answer 40

good for you :D

Answer 41

bye thank u so much