If (2+x/3)^55 is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive terms of the expansion are equal, then these terms are :

Coefficient of xr and xr+1 are equal.
Coefficient of Tr+1 = Coefficient of Tr+2
⇒ 55Cr(2)55-r(1/3)r = 55Cr+1(2)54-r(1/3)r+1
55!/(55-r!r!)(2) = 55!/(54-r!(r+1)!)(1/3)
⇒ 6(r+1) = 55-r ⇒ r=7
So, the terms will be 8th and 9th