A sequence of daily depth changes in a reservoir, x1,x2,x3,…x_1, x_2, x_3, \dotsx1,x2,x3,…, is defined by the recurrence relation
xn+1=2(xn+2)2−10 x_{n+1} = 2(x_n + 2)^2 - 10 xn+1=2(xn+2)2−10 x1=k−2 x_1 = k - 2 x1=k−2where kkk is a constant.
Find an expression for x2x_2x2 in terms of kkk, giving your answer in simplest form.
Given that ∑n=13xn=k+22\sum_{n=1}^{3} x_n = k + 22∑n=13xn=k+22
find the possible values of x2x_2x2.
