1. Two geometric means between 6 and 162.
6, __, __, 162
2. Two geometric means between 10 and -270.
10, __, __, -270
3. Three geometric means between 6 and 96.
6, __, __, __, 96
4. Three geometric means between 2 and 162
2, __, __, __, 162
5. Three geometric means between 8 and 648
8, __, __, __, 162
6. Four geometric means between 1/2 and 16
1/2, __, __, __, __, 16
7. Four geometric means between 4 and -972.
4, __, __, __, __, -972
8. Four geometric meons between 5 and 5120
5, __, __, __, __, 5120
9. Five geometric means between 1/9 and 81.
1/9, __, __, __, __, __, 81
10. Six geometric means between 2 and 4374.
2, __, __, __, __, __, __, 4374
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1. 18 and 54
Sol. 162=6r⁴⁻¹
162=6r³
162/6 = 6r³/6
27 = r³
³√27 = ³√r³
3 = r
2. -30 and 90
Sol. -270=10r⁴⁻¹
-270=10r³
-270/10 = 10r³/10
-27 = r³
³√-27 = ³√r³
-3 = r
3. 12, 24, 48
Sol. 96=6r⁵⁻¹
96=6r⁴
96/6 = 6r⁴/6
16 = r⁴
⁴√16 = ⁴√r⁴
2=r
Answer:
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