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find the missing terms in the following arithmetic or geometric (a). -1, -2, __, -8, __ (b). __, -81, 27, __, 3

User Nykakin
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1 Answer

3 votes

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.

User Poulami
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