Question

Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.
I'm not sure how to figure out if a sequence is a function or not... I know each number is becoming larger by 1. How do I explain that it is a function?

Answer 1

a sequence is a function by default, for any given nth term, you only have 1 possible value.

if i ask you for the 37th term, you can only give me 1 value
if i ask you for the 24th term, you can only give me 1 value
if i ask you for the 5th term, you can only give me 1 value

Answer 2

can we define a rule for the function? maybe, but a rule is not the same thing as a "function"

lets try a difference tier

5, 6, 8, 11, 15, 20, 26, 33, 41
1 2 3 4 5 ...
1 1 1 1 <-- we have a constant row, we can rule this as a quadratic

5 + n + n(n-1)/2

Answer 3

So how because the sequence is steadily increasing by 1, thats how it is a function.

Answer 4

ahhh I see

Answer 5

But what I'm confused about is how to write the sequence in function form. How do I write the function to show that it is increasing by 1?

Answer 6

a function is simply defined as: for any given input, there is only one output that can result.

Answer 7

I know

Answer 8

the method i used to see the function relies on finding a common difference

the rows express the value i had to add to get to the next term

Answer 9

but how to do I write it that way?

Answer 10

like you wrote: 5 + n + n(n-1)/2
to define your function as a sequence. Thats what I dont know how to do

Answer 11

its hard to describe the logic behind the method i used .... its easy to do tho

a difference tier, define the difference between each term

5, 6, 8, 11, 15, 20, 26, 33, 41
1 2 3 4 5 <-- not a constant, go down a row
1 1 1 1 <-- we have a constant row, we can rule this

using the beginning of each row, we can setup a rule

5 + 1n + 1 n(n-1)/2

the n parts are related to pascals triangle in some fashion, and as is, n starts at 0

Answer 12

Someone else said that this is how to write my sequence as a function:
f(n) = 5 + (n)(n - 1)/2
Is that right?

Answer 13

another way to view this is: since it takes 2 rows to get a constant value, we need a quadratic rule:

ax^2 + bx + c = y .... we can develop a system of 3 equations to solve as well

Answer 14

It makes sense to me, minus the /2 part..

Answer 15

do we know if you material defines n as starting at 0 or 1?

Answer 16

Thats all the info they give me. I guess they assume it starts at 5. So when I define the sequence as a function, I start at 5

Answer 17

the start of n does not refer to the start of the sequence

the start of n helps to define the rule. for some value of n, the term t has a value
.........................................
if n starts at 0, we can develop a set of ordered pairs as

n: 0, 1, 2, 3, 4, 5, 6, 7, 8
t: 5, 6, 8, 11, 15, 20, 26, 33, 41
...........................................

if n starts at 1, we can develop a set of ordered pairs as

n: 1, 2, 3, 4, 5, 6, 7, 8, 9
t: 5, 6, 8, 11, 15, 20, 26, 33, 41


the only difference in in how the rule is defined