A sequence $a_1, a_2, a_3, \dots\,$ is defined by

$an+1=k−anana_{n+1} = \dfrac{k - a_n}{a_n}$

where $k\,$ is a constant. The sequence is periodic of order 3 and $a_1 = 3$ .

Show that $k^2 - 11k - 12 = 0$ .

For this sequence, explain why $\neq 12$ .

Find the value of $∑r=1100ar\sum_{r=1}^{100} a_r$ .

A sequence $a_1, a_2, a_3, \dots\,$ is defined by

$an+1=k−anana_{n+1} = \dfrac{k - a_n}{a_n}$

where $k\,$ is a constant. The sequence is periodic of order 3 and $a_1 = 3$ .

Show that $k^2 - 11k - 12 = 0$ .

For this sequence, explain why $\neq 12$ .

Find the value of $∑r=1100ar\sum_{r=1}^{100} a_r$ .

1 Pure Mathematics

1 Pure Mathematics Questions