Question

I need help with my CC Algebra Sequence HW.

Find the next 4 four terms in the sequence
-1,-2,-3,-4..... Of course that is -5,-6,-7,-8 right?

So how do I write the explicit formula

Find a62

find f(10)

Please help me I am stressing out so much over my homework

Answer 1

is it arithmetic, geometric, or other?

Answer 2

arithmetic

Answer 3

good, we can either use the formula for it, or develop the formula for it

Answer 4

we can see that:\[f(n)=f(n-1)-1\]it is given to us that
\[f(0)=given\]
\[f(1)=f(0)-1\]
\[f(2)=f(1)-1\\~~~~~~=f(0)-1-1\\
~~~~~~=f(0)-2\]

\[f(3)=f(2)-1\\~~~~~~=f(0)-2-1\\
~~~~~~=f(0)-3\]

the pattern i see developing is explicitly defined as: \[f(n)=f(0)-n\]

Answer 5

well, f(0) = -1, so the explicit should use that instead of f(0)

Answer 6

but then different textbooks start n at different points. i started at n=0, many texts like to start n at 1, which is just a shift

Answer 7

f(n) = -1 - (n-1) is one way many texts would define it

Answer 8

So how would I solve the problem, Its very difficult for me to understand. I also very much appreciate
you helping me

Answer 9

first, figure out where you are expected to start n from; 0 or 1

then its just a matter of working thru develop a formula that works.

if n starts at 1; it is easy to see that

f(1) = -1
f(2) = -2
f(3) = -3
...
f(n) = -n



if n starts at 0; it is easy as well to see that

f(0) = -1
f(1) = -2
f(2) = -3
f(3) = -4
...
f(n) = -(n+1)

Answer 10

Again Its very hard for me to understand it, Is there any way you can put it to help me better.

Answer 11

In class I knew how to do it, and even in extra help I did. now for some reason I seemed to forget

Answer 12

I just need like a refresher if you know what I mean

Answer 13

i dont think so, it is rather simplistic to me and I cannot see where you would be having issues at. Can you tell me what is confusing you?

Answer 14

How do I find the the explicit formula for my problem

Answer 15

find a rule or pattern that is being expressed by the sequence. For this particular sequence of numbers that pattern is hopefully self explanatory. If it is form that is confusing:

implicit defines each new term by the other terms, but has to define some initial terms to start with:\[f(n)=f(n-1)-2f(n-2)\\f(0)=1,~f(1)=7\]using this information we can then find f(2,3,4,5,...)


an explicit formula is a form that simply find the nth term by using the value of n
\[f(n)=2^n+3n\]this way we do not need to know any initial values since any value of n defines the nth term

Answer 16

the pattern that shows up in your problem is easy to define explicitly:

f(n) = -n ; assuming n starts at 1

Answer 17

ok

Answer 18

Let me try it, and ill let you know if I need any more assistance

Answer 19

Thanks you so much !!

Answer 20

i might have to go home soon so if im not around, feel free to ask others as well :)

Answer 21

Ok thank I will let you know