Question

Find the first five terms of the sequence given by a1 = 2, an = -3an-1

Answer 1

The trick here is to sum the differences.an+1−an=2nan+1−an=2na100−a99=2⋅99a100−a99=2⋅99a99−a98=2⋅98a99−a98=2⋅98a2−a1=2⋅1a2−a1=2⋅1a100−a1=2(1+2+…99)a100−a1=2(1+2+…99)a100=2+9900=9902a100=2+9900=9902lol enjoy