Geometric progression 4

8,4√2,4,2√2

Correct result:

q =  0.7071
a₅ =  2
a₆ =  1.4142
a₇ =  1

Solution:

$$\begin{gathered} a_1=8 \\ {a}_2=4\cdot \sqrt{2}=4\sqrt{2}\doteq 5.6569 \\ {a}_3=4 \\ {a}_4=2\cdot \sqrt{2}=2\sqrt{2}\doteq 2.8284 \\ {q}_1=a_2\mathrm{/}{a}_1=5.6569\mathrm{/}8\doteq 0.7071 \\ {q}_2=a_3\mathrm{/}{a}_2=4\mathrm{/}5.6569\doteq 0.7071 \\ {q}_3=a_4\mathrm{/}{a}_3=2.8284\mathrm{/}4\doteq 0.7071 \\ {q}_1=q_2=q_3 \\ q=q_3=0.7071 \end{gathered}$$

$a_5=q\cdot a_4=0.7071\cdot 2.8284=2$

$a_6=q\cdot a_5=0.7071\cdot 2=\sqrt{2}=1.4142$

$a_7=q\cdot a_6=0.7071\cdot 1.4142=1$

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