- A sequence \(a _ { 1 } , a _ { 2 } a _ { 3 } , \ldots\) is defined by
$$a _ { n + 1 } = 5 - p a _ { n } \quad n \geq 1$$
where \(p\) is a constant.
Given that
- \(a _ { 1 } = 4\)
- the sequence is a periodic sequence of order 2.
a. Write down an expression for \(a _ { 2 }\) and \(a _ { 3 }\).
b. Find the value of \(p\).
c. Find \(\sum _ { r = 1 } ^ { 21 } a _ { r }\)