sequence of two

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Sat Jul 09, 2011 7:27 am

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?

1
2
4
6
9

Please help me.

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Source: Beat The GMAT — Problem Solving | Sat Jul 09, 2011 7:27 am

amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Sat Jul 09, 2011 10:06 am

s4= 2222
thus 2+22+222 means units place sum = 2*3
tens place sum = 2*2
and hundreds place sum = 2*1.

using the same concept and the carry overs

units place (1st) = 2*30 = 60
tens place (2nd)= 2*29+6(carry over) ...
fifth place (5th)= 2*26+5
............
............
9th place = 2*22+4
11th palce = 2*20+4

thus 4 it is.

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Sat Jul 09, 2011 12:01 pm

This is normal arithmetic way but is there any faster way?

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