Question

find the 90th term of the sequence 9,18,27...

Answer 1

1st term: 9
2nd term: 18
3rd term: 27

So you can see that this pattern is the list of multiples of 9

Answer 2

the first term is equal to 1*9 = 9
the second term is equal to 2*9 = 18
the third term is equal to 3*9 = 27
etc etc

Answer 3

so its 810?

Answer 4

you nailed it

Answer 5

yay!:) how do i find the missing term of 5,__,27

Answer 6

Is this an arithmetic sequence? or geometric sequence?

Answer 7

arithmetic

Answer 8

let d be the common difference

Answer 9

so to get the next term, we add on d to get 5+d

Answer 10

To get the next term after that, we add on another d

(5+d)+d = 5 + 2d

This is equal to 27 since we know this 3rd term

Therefore,

5+2d = 27

d = ??

Answer 11

11?

Answer 12

good

Answer 13

so the next term after 5 (the first term) is

5+d = 5+11 = 16

Answer 14

Notice how adding on another 11 gives us 16+11 = 27

Answer 15

how do you know if its arithmetic?

Answer 16

you just said it was when I asked you

Answer 17

I'm assuming they provided this information in the problem itself

Answer 18

a sequence is arithmetic when you add the same thing to each term to get the next term

Answer 19

no im on a different one now and it wants to know if its arithmetic or not

Answer 20

If its arithmetic you'll see that there's a common difference

Answer 21

so for instance, the sequence 1, 3, 5, 7, 9 is arithmetic because your'e adding 2 to each term to get the next term

Answer 22

the sequence 1, 3, 5, 7, 10 is NOT arithmetic because each term is found by adding 2 to the previous term...but jumping from 7 to 10 breaks this pattern

Answer 23

okay this is a new problem... 33,37,41 whats the 19th term... i know they have a difference of 4

Answer 24

first term: 33
common difference: 4

Answer 25

so

a1 = 33
d = 4

Answer 26

an = a1 + d(n-1)

an = 33 + 4(n-1)

an = 33 + 4n-4

an = 4n + 29

Answer 27

So the nth term is

an = 4n + 29

Answer 28

Notice for say term 2, n = 2

an = 4n + 29

a2 = 4(2) + 29

a2 = 8 + 29

a2 = 37

which matches up with the list

Answer 29

i got 105:)

Answer 30

There's a faster way instead of doing all of that. an = a1 + d(n – 1)

you want to find the 19th term so you put a_19 = 33 + 4(19-1)

a_19 = 33 + 4(18)
a_19 = 33 + 72
a_19 = 105

Answer 31

105 is correct

Answer 32

what about this one?

Answer 33

nevermind i got 5

Answer 34

5 is correct, nice work