I have a two arithmetic progressions (or arithmetic sequences):
- 2, 10, 18, ...
- 5, 8, 11, ...
They say to you that this two arithmetic sequences have 41 shared terms (terms I mean by $a_1$, $a_{45}$, for example). They ask:
At least how many terms are there in each sequence?
I don't know how to even begin. I don't know what to do.
As requested in comments:
Hint: Consider $$2,10,18,\mathbf{26},34,42,\mathbf{50},\ldots$$ and $$5,8,11,14,17,20,23,\mathbf{26},29,32,35,38,41,44,47,\mathbf{50},\ldots$$
the gaps between these and how many you need to get $41$ shared terms