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sequences help

can someone pls explain part d???? what i did was find the sum of the first 3 (1+(-1/2) +1) then multiplied it by 100/3 and i got an answer of 50 . why is this wrong?

plus this is not arithmetic so how did it use that rule
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Reply 1
Avatar for B_9710
B_9710
18
Write out the first 4 terms, notice anything?
The sequence repeats every 4 terms, 1,-1/2,1,-1/2 ...
If we are summing the first 100 terms then how many lots of this sequence is there?
(edited 8 years ago)
Original post by pondsteps
can someone pls explain part d???? what i did was find the sum of the first 3 (1+(-1/2) +1) then multiplied it by 100/3 and i got an answer of 50 . why is this wrong?

plus this is not arithmetic so how did it use that rule


the first 3 terms as they are in the sequence don't repeat i.e in this sequence the first 3 terms goes 1, -0.5, 1

when you add the first 3 terms multiply by 100 then divide by 3 you are assuming the sequence goes like this

[1,-0.5,1,][1,-0.5,1] etc etc
because you've assumed the firts 3 terms repeat one after another, but they don't

an arithmetic sequence is one where the difference between the terms is constant
Original post by pondsteps
can someone pls explain part d???? what i did was find the sum of the first 3 (1+(-1/2) +1) then multiplied it by 100/3 and i got an answer of 50 . why is this wrong?

plus this is not arithmetic so how did it use that rule


There should either be a general pattern in terms or it may be an arithmetic

What is
Unparseable latex formula:

X_1, X_2 & X_3

?
Original post by EqualRights
There should either be a general pattern in terms or it may be an arithmetic

What is
Unparseable latex formula:

X_1, X_2 & X_3

?


fist term second term and third term
Original post by thefatone
the first 3 terms as they are in the sequence don't repeat i.e in this sequence the first 3 terms goes 1, -0.5, 1

when you add the first 3 terms multiply by 100 then divide by 3 you are assuming the sequence goes like this

[1,-0.5,1,][1,-0.5,1] etc etc
because you've assumed the firts 3 terms repeat one after another, but they don't

an arithmetic sequence is one where the difference between the terms is constant

ohhh... thank u sooo much!! xxx
Original post by thefatone
fist term second term and third term


no omg, I meant as in values haha :biggrin:
Original post by EqualRights
There should either be a general pattern in terms or it may be an arithmetic

What is
Unparseable latex formula:

X_1, X_2 & X_3

?


okay so i can use the rule 1/2 (n) (a+L) even if the sequence is not arithmetic??
Reply 8
Avatar for B_9710
B_9710
18
Original post by pondsteps
okay so i can use the rule 1/2 (n) (a+L) even if the sequence is not arithmetic??


No. That only works for arithmetic sequences.
Original post by B_9710
No. That only works for arithmetic sequences.


umm but the above example is not arithmetic ... and i thought it was only for arithmetic
Reply 10
Avatar for Zacken
Zacken
22
Original post by pondsteps
umm but the above example is not arithmetic ... and i thought it was only for arithmetic


Exactly, so you can't use that formula.
Original post by Zacken
Exactly, so you can't use that formula.


lol but the markscheme said accept and it worked 😁
Reply 12
Avatar for B_9710
B_9710
18
The first 2 terms sum to 1/2 and there are 50 of them so the full sum is 25.
Reply 13
Avatar for Zacken
Zacken
22
Original post by pondsteps
lol but the markscheme said accept and it worked 😁


Yes, the original sequence isn't arithmetic but you can sum every two terms and treat it as an arithmetic (common difference 0) sequence with 50 terms.
Original post by EqualRights
no omg, I meant as in values haha :biggrin:

well first term is given as 1 then use the reccurence relation to fin the next 2 ^-^

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