Question

If a,b,c,d are consecutive terms of an arithmetic sequence, which of the following must be true?
I. b-a=d-c
II. d,c,b,a are consecutive terms of an arithmetic sequence.
III. a 12 years ago

Answer 1

you can use the same idea, rename
a,b,c,d as
a, a+x , a+2x , a+3x

Answer 2

b-a = x
d-c = x
I is correct

Answer 3

how about II and III?

Answer 4

yes, I. is correct. It is almost the definition of an arithmetic sequence: the difference between two successive terms is always the same

Answer 5

and II is correct?

Answer 6

For II. write
a+3x, a+2x, a+x, a

the difference between terms is
-x, -x, -x

what do you think ?

Answer 7

correct, i think

Answer 8

yes, correct. A.P.s can go up or down.
see http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

Answer 9

and III?

Answer 10

if the common difference is negative, is III. true ?

Answer 11

correct , i think

Answer 12

you could have 3,2,1,0
with a common difference of -1

are you saying 2 is bigger than 3 (not where I live)

Answer 13

OMG@@

Answer 14

okay, I and II are correct...

Answer 15

yes, III. could be true, but not always.... if depends if the sequence is going up or going down

Answer 16

so III. is not always true.

Answer 17

that means it must not be always true

Answer 18

so still I and II must be true

Answer 19

yes

Answer 20

thx

Answer 21

yw

Answer 22

i will ask you other questions tmr if you are free. :)
million thanks