Question

Here are some numbers

10 13 15 20 27 30

10 15 20 is tan arithmetic progression

Use three if the numbers to make a different arithmetic progression

Describe the rule.

Answer 1

15, 27, 39

a[n] = a[n-1] +12; a[1] = 15

Explanation:

The terms of an arithmetic progression have a common difference.

There are numbers in the given list that have differences of 5, 7, 12. The numbers with differences of 5 have already been listed. Other possible sequences are ...

13, 20, 27 . . . . common difference of 7

15, 27, 39 . . . . common difference of 12

The rule for the latter sequence is "each term is 12 more than the last" and the first term is 15.