問一問 sequence 的問題

a1 = 2
a2 = 2 + (2 + 3)
a3 = 2 + (2 + 3) + (2 + 2 x 3)
a4 = 2 + (2 + 3) + (2 + 2 x 3) + (2 + 3 x 3)
an = 2 + (2 + 3) + (2 + 2 x 3) + ... + [2 + (n - 1) x 3]
So an is the sum of the first n terms of an arithmetic sequence whose first term is 2 and common difference is 3.
Therefore:
an = 2 + (2 + 3) + (2 + 2 x 3) + ... + [2 + (n - 1) x 3]
= (n/2)[2 x 2 + (n - 1) x 3]
= 2n + 3n(n - 1)/2

Thanks for your further explanation !

Whereas 2n+ 3n(n-1)/2 follows well from the analysis of the multiples of 2 and multiples of 3 in the nth number, one more step to present it in the simpler form of n(3n+1)/2 will make the calculation easier.

勁!咁都睇到~