Sequence of two's...HELP!!!

[shriti]

S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk-1 + 2(10k-1). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?

a.1
b.2
c.4
d.6
e.9

[maihuna]

Let me try:
Last digit will be 2*30 having a cvarry of 6
next 2*29+6 6
2*28+6 6
2*27 + 6 6
2*26+6 5
2*25+5 5
2*24+5 5
2*23+5 5
2*22+5 4
2*21+4 4
2*20+4 4 and unit digit of 4

so I got the 11th digit as 4 though agree I have done exhaustive listing

[shriti]

yes that is the answer, but i was hoping for a quick solution..

thanks