Question

first term of the arithmetic sequence is 13. two other terms of the sequence are 37 and 73. common difference is consecutive terms integers. determine all possible values for 100th term.

Answer 1

after this, if you want help on more of these sequence problems, how about showing where you get stuck, or the answer you want to confirm?

If you are trying to say that the commons difference is an integer, then we know it is positive, and divides 73-37=36

so, the difference may be 1,2,3,4,6,9,12,18

However, d must also divide 37-13=24
and 73-13=60

That narrows our choices to 1,2,3,4,6,12

d T100
1 13+1*99=112
2 13+2*99=211
3 and so on
4
6
12

Answer 2

thank you