The recurrence cn=5cdotcn−1c_n = 5 \\cdot c_{n-1}cn=5cdotcn−1 with c0=1c_0 = 1c0=1 has closed form:
cn=5n−1c_n = 5^{n-1}cn=5n−1
cn=n+5c_n = n + 5cn=n+5
cn=ncdot5c_n = n \\cdot 5cn=ncdot5
cn=5nc_n = 5^ncn=5n