The rule for the nth term

Difficulty Stretch · Set ukq3io

Write the rule for the nth term of each sequence, the n term first, like 3n + 2.

Fill in what you can and press Check. Nothing you type is sent anywhere.

1
17, 8, -1, -10, -19, …
2
9, 4, -1, -6, -11, …
3
14, 11, 8, 5, 2, …
4
1, -3, -7, -11, -15, …
5
16, 10, 4, -2, -8, …
6
6, 0, -6, -12, -18, …
7
1, -8, -17, -26, -35, …
8
8, -1, -10, -19, -28, …
9
8, 3, -2, -7, -12, …
10
18, 13, 8, 3, -2, …
11
5, -4, -13, -22, -31, …
12
14, 5, -4, -13, -22, …
13
17, 9, 1, -7, -15, …
14
11, 9, 7, 5, 3, …
15
1, -3, -7, -11, -15, …
16
2, -1, -4, -7, -10, …
17
9, 2, -5, -12, -19, …
18
4, -4, -12, -20, -28, …
19
4, 0, -4, -8, -12, …
20
17, 9, 1, -7, -15, …

What is in this set

The numbers in this set run from 1 to 35.
Every problem in it will run downwards.
A careful solution takes 3 written steps on average.
The mistake this set invites most often, in 100% of the problems: the first term was used as the number on the end.
Answers are a short answer exactly as the problem asks for it.

Drawing 240 problems from this page produced 121 different ones, 50% — so a sheet of 20 will come back to a problem you have seen — there are only so many sensible ones of this kind.

The same skill, harder or easier

We would put this in front of a grade 8 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.