Question

Please help, I don't know how to solve these at all.
Find the first five terms of each sequence:
a_n= 1/2a_n-1 , where a_1=20

Answer 1

@abb0t will you please help me if you have time?

Answer 2

the first term is given to you, what is the first term?

Answer 3

after that, what is confusing you about the rule that they state?

Answer 4

I don't understand really anything on this math unit I'm doing such as explicit and recursive sequences and that was all the information given to me for that specific problem.

Answer 5

we want to find:

a1 a2 a3 a4 a5

we are given the value of a1, and a rule that defines how each new term is calculated.

a_n = 1/2 a_n-1
------------------

what is a_2? let n=2

a_2 = 1/2 a_1
-------------------
what is a_3? let n=3

a_3 = 1/2 a_2
-------------------

etc ...

Answer 6

So a is replaced by n?

Answer 7

a is the name of a function, that function takes on the values of n.

are you comfortable with the f(x) notation? if so, this is just an a(n) equivalent

Answer 8

Ok so f(9) for example would be the same as n(9), correct?

Answer 9

if we wanted to find the value of a function f(x), when x=9, then we would use the notation f(9)

all that has changed in this case is the name of the function, and the domain that we can use.

f changes to a

x changes to n

f(x) becomes a(n)

Answer 10

Ok I see so it's basically the same type of problem just different variables, Thanks for the help!

Answer 11

if you want to use f(x), then lets use it:

f(x) = 1/2 f(x-1)

given that f(1) = 20, what is f(2)?

f(2) = 1/2 f(2-1)
f(2) = 1/2 f(1)
^^ but we know f(1) = 20 therfore

f(2) = 1/2 * 20 = 10

Answer 12

f(3) = 1/2 f(3-1)
f(3) = 1/2 f(2)
^^ but we know f(2) = 10

f(3) = 1/2 * 10 = 5

and it just goes on from there in the same way

Answer 13

Ok so it decreases by intervals of 5.

Answer 14

well, each new terms is half of the previous one

Answer 15

20 to 10 is not a decrease of 5 :)

Answer 16

I'm sorry I meant how it decreases from 20 to 10 that's a decrease of 10 then from 10 to 5 is a decrease of 5, both 10 and 5 are divisible by 5 (I think that's the correct term) lol

Answer 17

thats a side trivia yes.

but 5/2 is not divisible by 5 so thats not really a pattern worth sticking your guns to is all

a1 = 20
a2 = half of 20 = 10
a3 = half of 10 = 5
a4 = half of 5 = 2.5
a5 = half of 2.5 = ____ well the last term we need to find.

Answer 18

which is 2 and you keep plugging in the numbers to find the values?

Answer 19

our rule is simple

what ever the last term we found was, the next term is half of it.

\[\underbrace{a_n}_{\large new~term} = 1/2 ~ \underbrace{a_{n-1}}_{\large prior~term}\]

Answer 20

Ok I think I get it now and if it was a 2 instead of 1/2 the value would be 2 more than what it was originally right?

Answer 21

correct

Answer 22

Ok got it I believe I was just trying to overthink the problem, thanks for the help :)

Answer 23

:) youre welcome.