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Mathematics 20 Online
OpenStudy (anonymous):

What is the 185th digit in the following pattern 12345678910111213141516.... (A ) 0 (B) 5 (C) 7 (D) 8 (E) 9

OpenStudy (anonymous):

A is 0

OpenStudy (dtan5457):

Can you see what the pattern is?

OpenStudy (anonymous):

yes

OpenStudy (dtan5457):

Then what's troubling you?

OpenStudy (anonymous):

everything

OpenStudy (dtan5457):

Tell me what the pattern is, lol.

OpenStudy (anonymous):

it is counting up with by 1s

OpenStudy (anonymous):

Lol relax relax this is simple you could do it :)

OpenStudy (dtan5457):

did you try writing out the rest of the digits.?

OpenStudy (anonymous):

nope

OpenStudy (dtan5457):

Then do it. -.-

OpenStudy (anonymous):

OHHHHHHHHH ok

OpenStudy (swissgirl):

Thats a slow method though

OpenStudy (danjs):

The first 9 numbers have 1 digit the next more than enough have 2 digits each

OpenStudy (dtan5457):

it will take 5 minutes

OpenStudy (solomonzelman):

oh, I thought that every digit is a separate term in the sequence.... then: \(\large\color{blue}{d=1}\) and \(\large\color{blue}{a_1=1}\)

OpenStudy (swissgirl):

but a_10=1 so d isnt really 1

OpenStudy (danjs):

ok, but what would you do if they asked for the 8726394920123 th digit dtan?

OpenStudy (anonymous):

I got it is 7

OpenStudy (dtan5457):

i would get a lot of paper ready

OpenStudy (anonymous):

nope, just logic

OpenStudy (danjs):

haha, or you could sum it up in a inch long formula

OpenStudy (solomonzelman):

wait, so I initially thought correctly, then. it is, \(\large\color{black}{ 1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,1,6 }\)

OpenStudy (danjs):

just counting up 11 12 13 14 15 16

OpenStudy (perl):

there are how many 1 digit numbers, then how many 2 digit numbers, etc

OpenStudy (danjs):

^right

OpenStudy (anonymous):

1...10 = 11 numbers 11...20 =20 numbers start from1 21....30= 20 numbers. start from2 and so on... if you stop at "start from 8, you have 171th number, now just count your finger to get 185 th number.

OpenStudy (perl):

there are 9 one digit numbers there are 100 - 10 + 1 two digit numbers

OpenStudy (danjs):

http://oeis.org/

OpenStudy (solomonzelman):

no, I am thinking it is: \(\large\color{black}{ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 }\) and you need the 185th digit (not term but digit). so firstly you need to find where will the 185th digit be: 1) first 9 terms = 9 digits 2) + second 9 terms = 9 digits + 90 99 digits so far: we need 86 more digits each term goes by 2 digits, so this is 43 more term.

OpenStudy (solomonzelman):

So, it is going to be: the last digit of the \(\large\color{black}{ (9+9+43)th }\) term

OpenStudy (solomonzelman):

last digit of \(\large\color{black}{ 61st }\) term

jimthompson5910 (jim_thompson5910):

There are 9 one-digit numbers So that leaves 185 - 9 = 176 digits left over. Divide by 2 to get: 176/2 = 88 So there are enough digits to form 88 two-digit numbers. If you add 88 to 10, you get 10+88 = 98. However, going from 10 to 98 yields 89 numbers (98-10+1 = 89). To fix this, we just take a step back and land on 97 instead.

OpenStudy (solomonzelman):

yeah, we all have different interpretations of the question...

OpenStudy (danjs):

From 1 to 9 ---> 9 digits 185 − 9 = 176 We need 176th digit after the first 9 This will be 2nd digit of 88th number after 9 i.e. 2nd digit of 87 185th digit = 7

OpenStudy (perl):

there are no parentheses in the original expression above, so I separated each digit by a comma

OpenStudy (solomonzelman):

my interpretation is not any of the options, (because 1 is not a choice) so i guess I was wrong....

OpenStudy (perl):

here is a nice table for the list of digits from 1 to very large number http://oeis.org/A033307/b033307.txt

OpenStudy (perl):

note that the list starts at n=0, instead of n=1. so the 184th entry is going to be the 185th digit in the original question

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