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A sequence of terms is given as 3, 33, 333, 3333 What is the hundred

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Carcass
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A sequence of terms is given as 3, 33, 333, 3333 What is the hundred [#permalink] New post   Updated on: 03 Jun 2024, 02:25
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A sequence of terms is given as 3, 33, 333, 3333…… What is the hundreds digit of sum of the first 10 terms of this series?

A. 3
B. 5
C. 6
D. 7
E. 9


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D

Originally posted by Carcass on 15 May 2024, 00:42.
Last edited by Carcass on 03 Jun 2024, 02:25, edited 1 time in total.
Fixed OA
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Aashi404
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Re: A sequence of terms is given as 3, 33, 333, 3333 What is the hundred [#permalink] New post   03 Jun 2024, 02:18
1
I feel the answer should be D.7 if the question asks for the number that is at the hundredth place of the sum of the first 10 terms.
Even when calculating the exact value, the sum stands at 3,703,703,700
Carcass Kindly let me know in case I have misunderstood.
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Carcass
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Re: A sequence of terms is given as 3, 33, 333, 3333 What is the hundred [#permalink] New post   03 Jun 2024, 02:28
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No sir my bad. You are totally correct. I double-checked the answer and fixed it.

It is D

3
33
333
3333
--------------
+ 3333333333

When first 10 terms of this sequence are added, 3 is added 10 times (30) at units digit. Hence, in the sum, 0 is written at units place and 3 is carried over.

Now 3 is added 9 times at tens digit and there is one 3 from carry over (27 + 3). Hence, 0 goes to tens place in the sum and 3 is carried over again.

3 is added 8 times at hundreds digit and there is one 3 from carry over (24 + 3). Hence, 7 goes to hundreds place in the sum and 2 is carried over.

Hence, (D) is the answer.
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Re: A sequence of terms is given as 3, 33, 333, 3333 What is the hundred [#permalink] New post   28 Nov 2024, 13:15
Carcass, what is an alternative explanation to this problem? I have a hard time to comprehend how

When first 10 terms of this sequence are added, 3 is added 10 times (30) at units digit. Hence, in the sum, 0 is written at units place and 3 is carried over.

I cannot visually see.

Can you please share a link to problems of the same type?
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Re: A sequence of terms is given as 3, 33, 333, 3333 What is the hundred [#permalink] New post   29 Nov 2024, 00:38
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No sir I am sorry. I do not see another way to figure out the problem. Maybe is not there another way :?
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Re: A sequence of terms is given as 3, 33, 333, 3333 What is the hundred [#permalink]
29 Nov 2024, 00:38
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