nth term formula for pattern

[vyn]

i have trouble answering this nth term pattern problem. i've been stuck on this one question in my assignment for days now.

i can't seem to find the appropriate formula for it:



i've tried different formulas with different numbers like: 2n x 1, 4(n-1), n^2, (3n+1)/2, etc with no luck so far.

Thanks for any help

 

[tkhunny]

Why not make another row: Number of Distinct Points on the Circle.

 

[stapel]

View attachment 8299

i've tried different formulas with different numbers like: 2n x 1, 4(n-1), n^2, (3n+1)/2, etc with no luck so far.

What was your logical basis for trying things like n²? How did you arrive at this for a possible formula? Thank you!