Asked by shana
Suppose that the sequence x0, x1, x2... is defined by x0 = 1, x1 = 5, and xk+2 = 3xk+1+10xk for k≥0. Find a general formula for xk.
Answers
Answered by
Reiny
You have to be more precise in your notation, you probably meant:
x<sub> k+2 </sub> = 3x<sub> k+1 </sub> + 10x<sub> k </sub>
that is:
x<sub> 0 </sub> = 1 = 5^0
x<sub> 1 </sub> = 5 = 5^1
x<sub> 2 </sub> = 3(5) + 10(1) = 25 = 25(1) = 5^2
x<sub> 3 </sub> = 3(25) + 10(5) = 125 = 25(5) = 5^3
x<sub> 4 </sub> = 3(125) + 10(25) = 625 = 25(25) = 5^4
x<sub>5 </sub> = 3(625) + 10(125) = 3125 = 25(125) = 5^5
..... = 3(3125) + 10(625) = 15625 = 5^6
looks like x<sub> k </sub>= 5^k
x<sub> k+2 </sub> = 3x<sub> k+1 </sub> + 10x<sub> k </sub>
that is:
x<sub> 0 </sub> = 1 = 5^0
x<sub> 1 </sub> = 5 = 5^1
x<sub> 2 </sub> = 3(5) + 10(1) = 25 = 25(1) = 5^2
x<sub> 3 </sub> = 3(25) + 10(5) = 125 = 25(5) = 5^3
x<sub> 4 </sub> = 3(125) + 10(25) = 625 = 25(25) = 5^4
x<sub>5 </sub> = 3(625) + 10(125) = 3125 = 25(125) = 5^5
..... = 3(3125) + 10(625) = 15625 = 5^6
looks like x<sub> k </sub>= 5^k
Answered by
jo
does anyone have lesson 10 linear function test answers