Explanation:
(a) Arithmetic sequence:
To find the missing terms in the arithmetic sequence, you need to determine the common difference (d) between consecutive terms. Then, you can use the formula: nth term (an) = a + (n - 1) * d.
Given the sequence: -1, -2, __, -8, __
Common difference (d) = -2 - (-1) = -1
Using the formula:
2nd term (a2) = -1 + (2 - 1) * -1 = -2
4th term (a4) = -1 + (4 - 1) * -1 = -4
So, the missing terms are -2 and -4.
(b) Geometric sequence:
To find the missing terms in the geometric sequence, you need to determine the common ratio (r) between consecutive terms. Then, you can use the formula: nth term (an) = a * r^(n - 1).
Given the sequence: __, -81, 27, __, 3
Common ratio (r) = (-81) / 27 = -3
Using the formula:
1st term (a1) = -81 * r^(1 - 1) = -81 * 1 = -81
4th term (a4) = -81 * (-3)^(4 - 1) = -81 * (-3)^3 = -81 * -27 = 2187
So, the missing terms are -81 and 2187.