# Geometric progression 4

8,4√2,4,2√2

Result

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

#### Solution:

$a_{ 1 } = 8 \ \\ a_{ 2 } = 4 \cdot \ \sqrt{ 2 } = 4 \ \sqrt{ 2 } \doteq 5.6569 \ \\ a_{ 3 } = 4 \ \\ a_{ 4 } = 2 \cdot \ \sqrt{ 2 } = 2 \ \sqrt{ 2 } \doteq 2.8284 \ \\ \ \\ q_{ 1 } = a_{ 2 }/a_{ 1 } = 5.6569/8 \doteq 0.7071 \ \\ q_{ 2 } = a_{ 3 }/a_{ 2 } = 4/5.6569 \doteq 0.7071 \ \\ q_{ 3 } = a_{ 4 }/a_{ 3 } = 2.8284/4 \doteq 0.7071 \ \\ \ \\ q_{ 1 } = q_{ 2 } = q_{ 3 } \ \\ q = q_{ 3 } = 0.7071 \doteq 0.7071 = 0.707$
$a_{ 5 } = q \cdot \ a_{ 4 } = 0.7071 \cdot \ 2.8284 \doteq 1.9997 = 2$
$a_{ 6 } = q \cdot \ a_{ 5 } = 0.7071 \cdot \ 1.9997 = \dfrac{ 707 }{ 500 } = 1.414$
$a_{ 7 } = q \cdot \ a_{ 6 } = 0.7071 \cdot \ 1.414 \doteq 0.9997 = 1$

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