$C_{1}$=(a+b)*a
$C_{2}$=(a+b)*a(a+b)
$C_{3}$=(a+b)*a(a+b)(a+b)
$C_{k}$=(a+b)*a(a+b)........(a+b) [there are k-1 (a+b) terms appended after a]
Formal description=$M(Q, \sum, \delta, q0, F)$
Q={q0, q1,.........., qk}
$\sum$={a, b}
q0=initial state
F={qk}
transition: $\delta$(q0, b)=q0,
$\delta$(q0, a)=q0, $\delta$(q0, a)=q1
$\delta$(i-1, b)=qi, $\delta$(i-1, a)=qi for $2\leq i\leq k$