Final answer:
The nth term rule for the given quadratic sequence is 2n² + 3n. To find the position of term value 605 in the sequence, one needs to solve the quadratic equation 2n² + 3n = 605 for n.
Step-by-step explanation:
To find the nth term rule of a quadratic sequence, we need to observe the pattern of the sequence and come up with a formula that represents all the terms in the sequence. The given sequence starts with 5, 20, 45, 80, 125,... Each term seems to increase by an increasing odd number. To determine the general rule, let's use the concept that each term can be expressed as n terms that when simplified using series expansion yield a term related to n. After series of manipulations, it can be concluded that the nth term is of the form 2n² + 3n.
Finding the Position of the Term Value 605
To find the position of the term value 605 in the sequence, we substitute it into the formula of the nth term and solve for n. This gives us a quadratic equation which can be solved to determine the value of n that corresponds to the term 605. Therefore, the position of the term value 605 can be found using the quadratic formula or by factoring if possible. In this case, we would solve 2n² + 3n = 605 for n.