Question

1, 6, 12, 18... What are the next 3 numbers and how was this solved?

Answer 1

This is a VERY BAD question. It should read, "Provide 3 values that could continue this sequence and state how you selected them."

1) There are INFINITELY many solutions.
2) If you prove that you have a valid sequence and someone marks it wrong, give me their phone number and I will have a stern chat with them for their bad mathematics.
3) Forget the first two if you are currently studying a unit on Arithmetic Sequences.
4) If you ARE studying Arithmetic Sequences, are you SURE the first value isn't 0, rather than 1?

I like 1, 6, 12, 18, 23, 26, 26 using constant 3rd Differences, but that is only one possible solution.

Answer 2

Are you sure there's 2 26's?

Answer 3

And I don't know what you mean by using 3rd constant differences.

Answer 4

you sure the first term is "1" ?

Answer 5

Yes

Answer 6

some patterns can be created using tiers of differences.

if you hit a tier that has all the same values in it, then its a constant and you can stop. The rest of the construct is similar in concept to pascals triangle to construct a suitable explicit equation for the sequence.

1 6 12 18
1st differences 5 6 6
2nd differences 1 0
3rd differences -1


there is not enough given values to determine a suitable explicit equation from the tiers of differences, but we could assume if need by that the 3rd tier is constant at -1


1 6 12 18
5 6 6
1 0
-1 -1 -1 -1

and then we can add up the tiers

1 6 12 18
5 6 6
1 0 -1 -2 -3
-1 -1 -1 -1



1 6 12 18
5 6 6 5 3 0
1 0 -1 -2 -3
-1 -1 -1 -1



1 6 12 18 23 26 26
5 6 6 5 3 0
1 0 -1 -2 -3
-1 -1 -1 -1


but thats not really an adequate solution here since we dont really have a footing to make that 3rd tier assumption with

Answer 7

...but it's probably as adequate as whatever the question-writer (QR) had in mind, unless maybe that first value really is a zero (0).

Really, if you can justify and explain your answer, it should be counted as correct, no matter what the QR had in mind.