Question

is the Consider the expression a_n = 1 + n + n², AP .a

Answer 1

Consider the expression a_n = 1 + n + n²,
For n = 1, a₁ = 1 + 1 + 1 = 3
For n = 2, a₂ = 1 + 2 + 4 = 7
For n = 3, a₃ = 1 + 3 + 9 = 13
For n = 4, a₄ = 1 + 4 + 16 = 21
The first four terms are 3, 7, 13, 21.
The difference between each consecutive term is not same.
Hence this is not an A.P.