11 The \(n\)th term of a sequence is \(u _ { n }\)
The sequence is defined by
$$u _ { n + 1 } = p u _ { n } + 70$$
where \(u _ { 1 } = 400\) and \(p\) is a constant.
11
- Find an expression, in terms of \(p\), for \(u _ { 2 }\)
11
- It is given that \(u _ { 3 } = 382\)
11 - Show that \(p\) satisfies the equation
$$200 p ^ { 2 } + 35 p - 156 = 0$$
11
- (ii) It is given that the sequence is a decreasing sequence.
Find the value of \(u _ { 4 }\) and the value of \(u _ { 5 }\)
11 - The limit of \(u _ { n }\) as \(n\) tends to infinity is \(L\)
11 - Write down an equation for \(L\)
11
- (ii) Find the value of \(L\)