Which explicit formula generates the infinite sequence 2, 9, 28, 65, 126, ...?
a_n = n²
a_n = n² + 1
a_n = n³
a_n = n³ + 1

Solution:

The explicit formula which generates the infinite sequence 2, 9, 28, 65, 126, ….

2 can be expressed as (1)³ + 1

9 can be expressed as (2)³ + 1

28 can be expressed as (3)³ + 1

65 can be expressed as (4)³ + 1

126 can be expressed as (5)³ + 1

The next term would be (6)³ + l = 217

The explicit formula that generates the given sequence is n³ + 1.

Which explicit formula generates the infinite sequence 2, 9, 28, 65, 126, ...?

Summary:

The explicit formula generates the infinite sequence 2, 9, 28, 65, 126, .. is n³ + 1.