Answer:
The sequence is
- 1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4, ...
Each term is the sum of the consecutive numbers from 1 to that number.
The nth term is the sum of the first n numbers:
- aₙ = 1 + 2 + 3 + ... + n
- aₙ = 1/2n(1 + n) (formula for sum of the n terms of arithmetic progression with the first term of 1 and common difference of 1)
- aₙ = n(n + 1)/2
1) The number of circles in the nth pile is n(n + 1)/2
2) When n tends to infinity the number of circles tends to infinity
