The sequence of positive numbers $u_1, u_2, u_3, \ldots$, is given by
$u_{n+1} = (u_n - 3)^2$,
$u_1 = 1$ - Edexcel - A-Level Maths Pure - Question 4 - 2006 - Paper 1
Question 4
The sequence of positive numbers $u_1, u_2, u_3, \ldots$, is given by
$u_{n+1} = (u_n - 3)^2$,
$u_1 = 1$.
(a) Find $u_2, u_3$ and $u_4$.
(b) Write down the... show full transcript
Worked Solution & Example Answer:The sequence of positive numbers $u_1, u_2, u_3, \ldots$, is given by
$u_{n+1} = (u_n - 3)^2$,
$u_1 = 1$ - Edexcel - A-Level Maths Pure - Question 4 - 2006 - Paper 1
Step 1
Find $u_2$
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Answer
To find u2, we substitute u1=1 into the formula:
u2=(u1−3)2=(1−3)2=(−2)2=4.
Step 2
Find $u_3$
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Answer
Next, we find u3 using u2:
u3=(u2−3)2=(4−3)2=(1)2=1.
Step 3
Find $u_4$
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Answer
Now, we calculate u4:
u4=(u3−3)2=(1−3)2=(−2)2=4.
Step 4
Write down the value of $u_{10}$
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Answer
To find the pattern, notice that u2=4, u3=1, and u4=4. The sequence oscillates between 4 and 1. Thus, since u10 is even,
