Multiples of number 7 are written next to each other 7142128... Find 2017 digit.
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Multiples of number 7 are written next to each other 714212835… What is the 2020th digit?
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2 Answers

Satish Shingavekar
, works at Mathematics
Answered September 2, 2021 · Author has 463 answers and 143.7K answer views
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
Multiples of 7 = 7, 14, 21, 28, 35
It's in Arithmetic Progression, we have to find 2020th digit.
Here a=7, d=7, n = 2020
Here a=7, d=7, n = 2020nth term = a + (n-1)d
term = 7 + (2020–1)(7)
= 7 + 2019×7
= 7 + 14133
= 14140