Which describes the series: 3 + 9 + 2.7 + 8.1 + …?
arithmetic
geometric
neither arithmetic nor geometric
both arithmetic and geometric
2. Which describes the series: 240 + 144 + 86.4 + 51.84 + …?
arithmetic
geometric
neither arithmetic nor geometric
both arithmetic and geometric
1 Answer

1.
If the series was arithmetic, then 3 + x = 9, and 9 + x = 2.7, and 2.7 + x = 8.1, which is impossible.
If the series was geometric, then 3x = 9, and 9x = 2.7, and 2.7x = 8.1, which is impossible.
So the series is neither.
2.
If the series was arithmetic, then 240 + x = 144, and 144 + x = 86.4, and 86.4 + x = 51.84, which is impossible.
If the series is geometric, then 240x = 144, 144x = 86.4, and 86.4x = 51.84, which is true if x = 0.6
So the series is geometric.