Determine the first five terms defined in the sequence {1 + 2n + 3n2}Also find their associated sum.

To determine the first five terms in the sequence {1 + 2n + 3n^2}, we can substitute values of n starting from 1 and calculate the corresponding terms.

For n = 1: Term 1 = 1 + 2(1) + 3(1^2) = 1 + 2 + 3 = 6

For n = 2: Term 2 = 1 + 2(2) + 3(2^2) = 1 + 4 + 12 = 17

For n = 3: Term 3 = 1 + 2(3) + 3(3^2) = 1 + 6 + 27 = 34

For n = 4: Term 4 = 1 + 2(4) + 3(4^2) = 1 + 8 + 48 = 57

For n = 5: Term 5 = 1 + 2(5) + 3(5^2) = 1 + 10 + 75 = 86

The first five terms in the sequence are 6, 17, 34, 57, and 86.

To find their associated sum, we can add up these terms: Sum = 6 + 17 + 34 + 57 + 86 = 200

Therefore, the associated sum of the first five terms in the sequence is 200.