Question

In this sequence 1,22,333,4444,11,2222,333333,44444444,111,222222…… what is 2170th term?

Answer 1

sequence is 1, 22 , 333, 4444, 11, 2222, 333333, 44444444, 111, 222222, 333333333...

Let us consider first 4 terms at a time,

number of 1 = 1

number of 2 = 2

number of 3 = 3

number of 4 = 4

also we see 1st repeat after every 4 terms and number of 1st increased by 1.

so, divide 2710 by 4 ,

we get, 2710 = 677 × 4 + 2

means if we 2710 is divided by 4 , remainder will be 2 .

so, 2710 - 2 = 2708th term will be 1 { 111......1111(677 times)}

next 2709th term is {22...2222(677×2=1354 times)}

hence, 2710th term is 2