Question

Find the first 5 terms of the sequence: a1 = 500, an = (an-1)/5

Answer 1

We are given \[a_1 = 500, \ \ a_n = \frac{a_{n-1}}{5}\] and asked to find the first five terms. Is that the question?

Answer 2

yea

Answer 3

OK, this one is sort of easy and fun once you understand what all the formulas mean. :)

Answer 4

Im ready to take notes lol

Answer 5

Mathematicians use the \[a_n\] as a way to stand for the nth term. That is, \[a_1\] is the 1st term, \[a_2\] is the 2nd term, \[a_3\] is the 3rd term, and so on...

Answer 6

Does that make sense so far?

Answer 7

yes so i replace n with 1, 2, 3 etc?

Answer 8

Exactly! And you were already given the first term, that is, \[a_1 = 500\]

Answer 9

The other formula tells you how to find the next term.

Answer 10

So, \[a_n = \frac{a_{n-1}}{5}\] means to find the next term "an", take the previous term "an-1" and divide by 5

Answer 11

So, what happens when you plug in n = 2?

Answer 12

soo its 500-1/5 ?

Answer 13

Almost. :) Here's the way it works, you are close...

Answer 14

\[a_n = \frac{a_{n-1}}{5}\] when I plug in n = 2, I see \[a_2 = \frac{a_{2-1}}{5}\] which is \[a_2 = \frac{a_1}{5}\]

Answer 15

whats a ?

Answer 16

a isn't really anything by itself... a1 is the first term, a2 is the second term, a3 is the third term and so on, like we looked at before.

Answer 17

What the equation says is that a2 is equal to a1 divided by 5. Do you see that?

Answer 18

yea i see

Answer 19

In english, the second term is equal to the first term divided by 5.

Answer 20

but where does the 500 go ?

Answer 21

Good question!

Answer 22

So, since \[a_1 = 500\], we just get \[a_2 = \frac{a_1}{5}=\frac{500}{5}=100\]

Answer 23

See how it works?

Answer 24

kinda

Answer 25

It is a bit tricky at first, but you'll get it soon. :)

Answer 26

no then on the next one would be 100/5?

Answer 27

so*

Answer 28

Yes, that is right. The third term is the second term divided by 5 (according to the formula)

Answer 29

In math lingo, \[a_3 = \frac{a_2}{5}\]

Answer 30

So since \[a_2 = 100\] we have to have \[a_3 = \frac{100}{5} = 20\]

Answer 31

okay heres what i have so far 100, 20, 4, 4/5?

Answer 32

Those are the 2nd, 3rd, 4th, and 5th terms, good that is accurate.

Answer 33

and then 4/25?

Answer 34

That would be the 6th term, yes.

Answer 35

But the question only wants us to find the first 5 terms.

Answer 36

So, we just need the list for the 1st, 2nd, 3rd, 4th, and 5th terms.

Answer 37

oooh ! i get it ! 500 is the first

Answer 38

YES!!! :D

Answer 39

yay omgee i was putting the wrong answer :p

Answer 40

thank you so much (:

Answer 41

Oh, haha, I've done that before too. ;) no problem!

Answer 42

Good job, you are better at math than you think. :)

Answer 43

haha i just people to explain it to me :p cause i get so lost sometimes

Answer 44

You aren't the first to get lost... math class is made a lot harder than it needs to be... sometimes plain english is better than "math speak" :)

Answer 45

haha it is :p

Answer 46

thank you again

Answer 47

no problem, good night! :)