The seven numbers \(a, x_1, x_2, x_3, x_4, x_5, b\) are in arithmetic progression. Express \(x_2\) in terms of \(a\) and \(b\), and show that \(x_1+x_3+x_5=\dfrac{3}{2}(a+b)\).

Given also that the numbers \(a, x_2, b\) are in geometric progression, and that \(b\neq a\), express \(b\) in terms of \(a\).

Can we work out \(d\), the common difference in the arithmetic progression?