To find the eighth term in the sequence, we need to use a formula for the nth term. The sequence is not arithmetic or geometric, so we cannot use the standard formulas for those types of sequences. Instead, we need to find a pattern that relates the term number and the term value.
One way to do this is to look at the differences between consecutive terms. The differences are 3, 5, 7, 9, ... which form an arithmetic sequence with a common difference of 2. This means that each term is 2 more than the previous difference. We can use this information to write a formula for the nth term:
a_n = a_{n-1} + 2(n-1)
This formula says that the nth term is equal to the previous term plus 2 times the previous term number. To use this formula, we need to know the first term, which is 0. Then we can apply the formula repeatedly to find the next terms. For example, to find the second term, we have:
a_2 = a_1 + 2(1-1) = 0 + 2(0) = 0
To find the third term, we have:
a_3 = a_2 + 2(2-1) = 0 + 2(1) = 2
To find the eighth term, we need to repeat this process until we reach n = 8. Alternatively, we can use a calculator to evaluate the formula for n = 8. Either way, we get:
a_8 = a_7 + 2(7-1) = 35 + 2(6) = 47
Therefore, the eighth term in the sequence is 47.