The sum of an infinite geometric series is 162 and the sum of its first n terms is 160. If the inverse of its common ratio is an integer, then which of the following is/are possible first term/terms?

S∞=a1−r=162Sn=a1−rn1−r=160Solving these equations, we get1−rn=160162=8081⇒ 1−8081=rn⇒ rn=181or 1rn=81                  ……. (1)Now, it is given that 1r is an integer and n is also an integer.Hence, the relation (1) implies that 1r=3,9, or 81 so that n = 4, 2 or 1 accordingly.Therefore, (i) a=1621−13=108                 (ii) a=1621−19=144                 (iii) a=1621−181=160