Question

Sequences:

Answer 1

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