In a sequence of numbers a_{3} = 0a_{4} = 4; a_{5} = 8, a_{6} = 12 and a_{7} = 16 Based on this information , which equation can be used to find the n ^ (th) term in the sequence , ? a_{n}
The common difference between consecutive terms in this sequence is 4, so we can use the equation:
a_{n} = a_{3} + 4(n - 3)
This equation starts with a_{3} because the given information starts with a_{3} = 0. The term a_{3} corresponds to n = 3 in the sequence. By subtracting 3 from n, we can determine the number of terms that have elapsed since a_{3}, and then we multiply that number by the common difference of 4 to find the term at index n.