Five element

The geometric sequence is given by quotient q = 1/2 and the sum of the first six members S6 = 63. Find the fifth element a5.

Result

a5 =  2

Solution:

q=1/2=12=0.5 s6=63  s6=q61q1 a1  a1=s6 q1q61=63 0.510.561=32  a5=a1 q4=32 0.54=2q=1/2=\dfrac{ 1 }{ 2 }=0.5 \ \\ s_{6}=63 \ \\ \ \\ s_{6}=\dfrac{ q^6-1 }{ q-1 } \cdot \ a_{1} \ \\ \ \\ a_{1}=s_{6} \cdot \ \dfrac{ q-1 }{ q^6-1 }=63 \cdot \ \dfrac{ 0.5-1 }{ 0.5^6-1 }=32 \ \\ \ \\ a_{5}=a_{1} \cdot \ q^4=32 \cdot \ 0.5^4=2



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