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If \(a\left (n+1 \right )=1/2*a\left (n \right)+10\),and a(0)=50,find an expression for a(n) with n.

 Aug 22, 2016

Best Answer 

 #1
avatar+9466 
+17

a(0)=50

a(1)=1/2 x 50 + 10 = 35

a(2)= 1/2 x 35 + 10 = 55/2

a(3)= 1/2 x  27.5 + 10 =75/4

a(n) = \(50 - 30\overbrace{(1/2+1/4+1/8+.......)}^{n}\)\(50 - 30(\dfrac{2^n-1}{2^n})\)

 Aug 23, 2016
 #1
avatar+9466 
+17
Best Answer

a(0)=50

a(1)=1/2 x 50 + 10 = 35

a(2)= 1/2 x 35 + 10 = 55/2

a(3)= 1/2 x  27.5 + 10 =75/4

a(n) = \(50 - 30\overbrace{(1/2+1/4+1/8+.......)}^{n}\)\(50 - 30(\dfrac{2^n-1}{2^n})\)

MaxWong Aug 23, 2016

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