Question

PLEASE HELP.........


I need feedback on sequences because my teacher did not explain well at all. On explicit, recursing, and that sorta stuff.

Answer 1

@aum @ganeshie8 @Jhannybean @Abhisar @DJ3strella @Secret-Ninja @Kit_Kat_Nat_<3

Answer 2

Can anyone help?

Answer 3

\(Please\)

Answer 4

Can you explain sequences because I don't get them at all and that is very important in the unit I'm on.

Answer 5

A sequence is a list of numbers. for example
\[1, 4, 9, 16, 25, \ldots \]

Answer 6

\(\ldots \) tell you that the sequence goes on forever

Answer 7

how about explicit and recursive?? I'm very confused on those types of sequences.

Answer 8

each of the numbers in the list is referred to as a term
\[1, 4, \color{red}{9}, 16, 25, \ldots\]

\( \color{red}{9}\) is a term of above sequence

Answer 9

lets represent that sequence using both explicit and recursive formulas

Answer 10

yes please

Answer 11

First of all, do you see any pattern in above sequence ?

Answer 12

not really...

Answer 13

no

Answer 14

try again, there is a pretty obvious pattern

Answer 15

ok, can i tag you when i get it because im slow, o_o

Answer 16

is it ok?

Answer 17

its okay leave that sequence, lets use some other easy example

Answer 18

fine

Answer 19

How about this sequence
\[2,4,6,7,10,\ldots \]

Answer 20

2

Answer 21

do you see any pattern that helps you in predicting the next term ?

Answer 22

what do you mean by 2

Answer 23

add 2

Answer 24

right! you can get next term by adding 2 to present term, yes ?

Answer 25

yep

Answer 26

thats exactly same as the recursive formula of that sequence

Answer 27

oh ok now how about explicit?

Answer 28

\[\text{(next term)} = \text{(present term)} + 2\]

Answer 29

\[a_{n+1} = a_n + 2\]

Answer 30

oh yeah i remember that my teacher said that

Answer 31

and you start at \(\large a_1 = 2\)

Answer 32

so that would be recursive?

Answer 33

so the complete recursive formula for that sequence would be

\[\large a_{n+1} = a_n + 2, ~~a_1 = 2\]

Answer 34

yes do you see anything bad about recursive formulas in general ?

Answer 35

oh, get it, can you show me an explicit example?

Answer 36

recursive formulas look cute but they are not so great when you actually want to use them

Answer 37

Notice that you need to know the previous terms to find a specific term

Answer 38

suppose if I ask you for 20th term in above sequence and if you happen to have only a recursive formula, you need to find all the previous 19 terms first to tell me the 20th term

Answer 39

i see..yes i do.

Answer 40

so we prefer explicit formulas

Answer 41

explicit formula DIRECTLY gives you the "nth term"

Answer 42

well i want to see an example of it because i don't understand, for me it would be none.

Answer 43

oh

Answer 44

lets write an explicit formula for the same sequence
\[2,4,6,7,10,\ldots\]

Answer 45

heard of arithmetic sequence before ?

Answer 46

yes, and sorry i did not mention that one but i also need an explanation on that because seriously my teacher can't explain sometimes.

Answer 47

one thing at a time

Answer 48

but first of course this

Answer 49

yeah

Answer 50

I'll give you the explicit formula. You check if it works

Answer 51

ok

Answer 52

\[\large a_n = 2n\]

Answer 53

thats an explicit formula ^
see if you can find the 4th term using that formula