Multiples of 7 are written next to each other 714212835 . Find 2020th digit
Answers
Answer:Very Simple !
Count of number of various digit multiples of 7
(1) one digit ~ 7 i.e. only 1 ~ total digits written 1
(2) 2 digit ~ 14 to 98 i.e. 13 ~ total digits 2*13 = 26
(3) 3 digit ~ 105 to 994 i.e. 128 ~ digits 3*128 = 384
Upto 994 , number of total digits written is 411
We want 2020th digit & that will be 2020 — 411 = 1609 th digit after this now ! & that will be found in 403 th 4 digit number as 402 * 4 = 1608 digits hereafter will be written for next 402 four digit numbers & our required 1609 th digit will be 1st digit of our 403 th four digit number !
That 403 th four digit number is ~ Last 3 digit number 994 + 7*403 = 3815
3 is the 1st digit of this 403 th four digit number written at 2020 th place in our writting of 7 multiples !
So answer is digit 3
Given : Multiples of 7 are written next to each other 714212835...
To Find : 2020th digit.
Solution:
one digit number 7 one number = 1 digit
two digit numbers
14 to 98 13 numbers = 26 digits
three digit numbers
105 to 994 , 128 number , 384 digits
384 + 26 + 1 = 411 Digits
for 2020 th digit
2020 - 411 = 1609 Digits
1609 = 402 * 4 + 1
Hence 402 , 4 digit numbers and 1st digit of 403rd 4 digit number
4 digit numbers starts from 1001
1001 + (403 - 1) 7
= 3815
3815 first digit is 3
Hence 2020th digit. is 3
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