Number sequences, step by step
Two, six, eighteen, fifty-four — what comes next, and how did you know?
The question
Here are the first four terms of a number sequence. 7 12 17 22
Here are the first four terms of a number sequence. 7 12 17 22
7121722
7+10 × 5=57
7+10 × 5=57
(102 − 7)÷5=19
term20
- Both questions are the same rule read in opposite directions, so find the rule once. 7 to 12 is + 5, and it holds all the way along.
- What is the 11th term? Counting on would work and would stop working at the 80th term. From the 7 there are 10 steps to take: 7 + 10 × 5 = 57.
- Which term is 102? Same rule, undone: how many steps from 7 up to 102? 102 − 7 = 95, and 95 ÷ 5 = 19 steps — so it is term 20.
How it works.
- 01
Both questions are the same rule read in opposite directions, so find the rule once. 7 to 12 is + 5, and it holds all the way along.
- 02
What is the 11th term? Counting on would work and would stop working at the 80th term. From the 7 there are 10 steps to take: 7 + 10 × 5 = 57.
- 03
Which term is 102? Same rule, undone: how many steps from 7 up to 102? 102 − 7 = 95, and 95 ÷ 5 = 19 steps — so it is term 20.