Answer:
Arithmetic sequence: 6, 20, 34, 48
Geometric sequence: 6, 12, 24, 48
Explanation:
In an arithmetic sequence, terms are evenly spaced apart; in other words, consecutive terms have a common difference (d). For this problem, we can solve for the common difference with the equation:
6 + d + d + d = 48
6 + 3d = 48
3d = 42
d = 14
We can use this to find the middle terms:
6, 6 + d, 6 + 2d, 48
6, 6 + 14, 6 + 2(14), 48
6, 20, 34, 48
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In a geometric sequence, consecutive terms have a common ratio (r). For this problem, we can solve for the common ratio with the equation:
6 · r · r · r = 48
6 · r³ = 48
r³ = 8
r = 2
We can use this to find the middle terms:
6, 6r, 6r², 48
6, 6(2), 6(2)², 48
6, 12, 24, 48