Final answer:
The question asks for the geometric sequence that contains two terms between -9 and 820.125. By applying the geometric sequence formula and solving for the common ratio, we can calculate and find the entire sequence including the two terms in question.
Step-by-step explanation:
We are asked to find the geometric sequence that includes two terms between -9 and 820.125. To solve this, we will use the formula for a geometric sequence, which is a_n = a_1 × r^{(n-1)}, where a_n is the n-th term, a_1 is the first term, and r is the common ratio.
We know that a_1 = -9 and a_5 = 820.125 as we have three terms (including -9 and 820.125) between the first and the fifth term. Writing out what we know:
- a_1 = -9
- a_5 = -9 × r^{4} = 820.125
Dividing a_5 by a_1, we get r^{4} = 820.125 / -9. Solving for r, we find r = ∛(820.125 / -9), which gives us the common ratio r.
Then, we can compute the missing terms a_2, a_3, and a_4 by multiplying a_1 by r, r^{2}, and r^{3} respectively. This provides us with the full sequence with the two geometric terms located between -9 and 820.125.