Insert

Insert five numbers between 8 and 27 such numbers that, with two given ones, they form the first seven members of the geometric sequence.

Final Answer:

a₂ =  9.798
a₃ =  12
a₄ =  14.6969
a₅ =  18
a₆ =  22.0454

Step-by-step explanation:

$$\begin{gathered} a_1=8 \\ {a}_7=27 \\ {a}_7=a_1\cdot q^6 \\ q=\sqrt[6]{a_7/a_1}=\sqrt[6]{27/8}\doteq 1.2247 \\ {a}_2=a_1\cdot q=8\cdot 1.2247=4\sqrt{6}=9.798 \end{gathered}$$

$a_3=a_2\cdot q=9.798\cdot 1.2247=12$

$a_4=a_3\cdot q=12\cdot 1.2247=6\sqrt{6}=14.6969$

$a_5=a_4\cdot q=14.6969\cdot 1.2247=18$

$a_6=a_5\cdot q=18\cdot 1.2247=9\sqrt{6}=22.0454$

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