Geometric progression 4

8,4√2,4,2√2

Result

q =  0.707
a5 =  2
a6 =  1.414
a7 =  1

Solution:

a1=8 a2=4⋅ 2=4 2≐5.6569 a3=4 a4=2⋅ 2=2 2≐2.8284  q1=a2/a1=5.6569/8≐0.7071 q2=a3/a2=4/5.6569≐0.7071 q3=a4/a3=2.8284/4≐0.7071  q1=q2=q3 q=q3=0.7071≐0.7071≐0.707a_{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}/a_{1}=5.6569/8 \doteq 0.7071 \ \\ q_{2}=a_{3}/a_{2}=4/5.6569 \doteq 0.7071 \ \\ q_{3}=a_{4}/a_{3}=2.8284/4 \doteq 0.7071 \ \\ \ \\ q_{1}=q_{2}=q_{3} \ \\ q=q_{3}=0.7071 \doteq 0.7071 \doteq 0.707
a5=q⋅ a4=0.7071⋅ 2.8284≐1.9997≐2a_{5}=q \cdot \ a_{4}=0.7071 \cdot \ 2.8284 \doteq 1.9997 \doteq 2
a6=q⋅ a5=0.7071⋅ 1.9997=707500=1.414a_{6}=q \cdot \ a_{5}=0.7071 \cdot \ 1.9997=\dfrac{ 707 }{ 500 }=1.414
a7=q⋅ a6=0.7071⋅ 1.414≐0.9997≐1a_{7}=q \cdot \ a_{6}=0.7071 \cdot \ 1.414 \doteq 0.9997 \doteq 1

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