Question

1 2 2 3 3 3 4 4 4 4 1 1 2 2 2 2 3 3 3 3 3 3 4 what is the 2888th number in this sequence

Answer 1

Concept:

A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It has members, just like a set. The length of the sequence is defined by the number of entries.

Given:

A sequence is given to us 1 2 2 3 3 3 4 4 4 4 1 1 2 2 2 2 3 3 3 3 3 3 4

To find:

The 2888th number in this sequence

Solution:

1st series: 1,22,333,4444 no.of terms(n.o.t.)=10

2nd: 1,1,2222,333333,44444444 n.o.t=20

3rd: 1(3),2(6),3(12),4(15) n.o.t=30

sum of number of terms till nth series = 10+20+30+...10*n

= 10(1+2+3+4...+n)

=  10*n(n+1)/2

Required position = 2888

10*n(n+1)/2 <= 2888

if n = 23,

LHS = 2760 i.e., 128 more numbers to reach 2888 position

24th series: 1(24),2(48),3(72),4(96)

24+48=72 (less than 128)

24+48+72=144 (more than 128)

Thus, 3 should be at the 2888th position

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