Question

Please help! Will award medal!

Find an equation for the nth term of the arithmetic sequence. a19 = -92, a20 = 6

Answer 1

@Abhisar

Answer 2

do you know the formula for the n'th term of an arithmetic sequence?

Answer 3

alternatively, do you know what an arithmetic sequence is?

Answer 4

no and how would i use the 19th and 20th term anyway? @asnaseer

Answer 5

what is the property of an arithmetic sequence - what "makes it" an arithmetic sequence?

Answer 6

the pattern?

Answer 7

so adding 98?

Answer 8

correct - so an arithmetic sequence is a sequence you get by adding the same number to every term (the number you add could be negative)

Answer 9

in your case you are given the 19th and 20th terms, so you can say that:\[a_{20}=a_{19}+d\]where 'd' is the difference between each term in the sequence - make sense?

Answer 10

so 98?

Answer 11

correct - so now you know that this "common difference" is 98

You now need to recall the formula for the n'th term

Answer 12

ok so its -1856 and 98(n-1)

Answer 13

but is it + or - the 98(n-1)

Answer 14

imagine you had such a sequence:\[a_{1},a_{2},a_{3},...\]and you know that the common difference between them is 'd'. then you could rewrite this sequence as:\[a_1,a_1+d,a_1+2d,...\]agreed?

Answer 15

yes

Answer 16

if you compare this to the original sequence of: \(a_1,a_2,a_3,...\) you will notice that we can say that:\[a_n=a_1+(n-1)d\]this gives us the formula for the n'th term in the sequence

Answer 17

we already know what 'd' is but we do not yet know what \(a_1\) is equal to

Answer 18

so what you can do is use the information given to you - e.g. you are told that the 20th term is 6, therefore we can write:\[a_{20}=6=a_1+(20-1)d=a_1+(20-1)\times98\]

Answer 19

use this to work out what \(a_1\) is equal to

Answer 20

isnt it -1856

Answer 21

perfect!

Answer 22

now put it all together and we get:\[a_n=a_1+(n-1)d=-1856+(n-1)98\]

Answer 23

as a sanity check you could use this to see if \(a_{19}\) and \(a_{20}\) come out correctly

Answer 24

so -1856+98(n-1)

Answer 25

yes

Answer 26

cool thanks!

Answer 27

yw :)

Answer 28

i actually got it way earlier up there^ but you ended up explaining it cuz i was just guessing but thanks!

Answer 29

do you mind helping me with another one?

Answer 30

it's always better to understand the concepts - it will make solving the next one much easier :)

Answer 31

I need to go and eat now - but just post a new question and I'm sure there will be plenty of good people here to help you

Answer 32

haha okay thanks!