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How am I meant to solve B? I've done A it goes as follows:-

Sequences may be generated by recurrence relations of the form $U_{n+1}=kU_n-20, U_0=5.$

A) Show that $U_2=5k^2-20k-20$

B) Determine the range of values of K for which $U_2 \lt U_0.$

Thanks.

Community
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Johnson
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1 Answers1

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You want to find the values of $k$ for which $U_2 < U_0$:

$U_2 < U_0 \Leftrightarrow 5k^2-20k-20 < 5 \Leftrightarrow k^2 -4k-4 < 0$

Do you get how to solve the rest?

user9750060
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  • That's a great start, but sadly I don't can you explain further? – Johnson Oct 05 '17 at 06:49
  • You can assume that $k^2 - 4k - 4 = 0$, then factorise and solve for $k$. The values you will get for $k$ will be the lower and the upper bound of your 'range', lower $k$ will be strictly less than, and upper $k$ will be strictly greater than. Do this: plot $x^2 - 4x -4$, then you will get an idea of which x-values make the expression negative. Does this help? – user9750060 Oct 05 '17 at 07:40