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find an expression for a(n) with using variable n

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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.

fiora Aug 22, 2016

Best Answer

+9675

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

MaxWong Aug 23, 2016

1⁺⁰ Answers

+9675

+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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