The first term of an arithmetic sequence is 1, another term of the sequence is 91 and all of the terms of the sequence are integers. How many distinct arithmetic sequences meet these three conditions?
thank you in advance
The sequences with the following terms are:
First term = 1
nth term = 91
All term must be integers.
Common difference 91 as a term
1 91st. term
2 46th term
3 31st term
5 19th term
6 16th term
9 11th term
10 10th term
15 7th term
18 6th term
30 4th term
45 3rd term
90 2nd term
As you can see, there are 12 sequences which start at 1 and have 91 as one of terms and are all integers.
