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In a seqIn a sequence, nth term: a_n = 4+10uence , nth term: a nth =4+

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GMAT 1: 580 Q44 V28
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In a seqIn a sequence, nth term: a_n = 4+10uence , nth term: a nth =4+  [#permalink]

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New post Updated on: 04 Apr 2019, 20:59
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

53% (01:42) correct 47% (01:58) wrong based on 15 sessions

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In a sequence, \(n_{th}\) term: \(a_n = 4+10*a_{n-1}\) and \(a_1 = 4\), find the hundred's digit of the sum of first 10 terms.

A. 5
B. 4
C. 3
D. 6
E. 0

Originally posted by dharam44 on 04 Apr 2019, 10:43.
Last edited by Bunuel on 04 Apr 2019, 20:59, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In a seqIn a sequence, nth term: a_n = 4+10uence , nth term: a nth =4+  [#permalink]

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New post 04 Apr 2019, 11:37
a1=4; a2= 4+10*(4-1)=34
Similarly, a3 = 334;a4= 3334
Unit place digit is always 4, sum is 34+334+3334+33334+333334+----so on
I am getting 7 as hunndred's place digit.
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Re: In a seqIn a sequence, nth term: a_n = 4+10uence , nth term: a nth =4+  [#permalink]

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New post 05 Apr 2019, 03:16
ankitpareek23 wrote:
a1=4; a2= 4+10*(4-1)=34
Similarly, a3 = 334;a4= 3334
Unit place digit is always 4, sum is 34+334+3334+33334+333334+----so on
I am getting 7 as hunndred's place digit.


a2=4 + 10(a1)= 44 not 34, however i feel like you might be on the right track otherwise, whats your thinking? I couldn't find a way to solve this quick enough
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Re: In a seqIn a sequence, nth term: a_n = 4+10uence , nth term: a nth =4+  [#permalink]

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New post 05 Apr 2019, 06:15
So the first term is 4. The second one is 4+10*4=44 the third one is 4+10*44=444, 4th one 4+10*444= 4444 and then we can see the pattern. Since we are only asked the hundreds digit we can simply do 444*8 (last 8 terms) and add the first two

So its 444*8 + 44 +4= 3600.

Therefore the option is D
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Re: In a seqIn a sequence, nth term: a_n = 4+10uence , nth term: a nth =4+   [#permalink] 05 Apr 2019, 06:15
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