Answer to Question #170524 in Calculus for Aiman Anwar

Question

How can we produce the terms of a sequence if the first 10 terms are 1, 2, 2, 3, 3, 3, 4, 4, 4, 4?

Answer 1

the series is like

1,2,2,3,3,3,4,4,4,4...and we have to find 100th position

so to this series 1 is coming at 1st position

2 is repeating until 3rd position

3 is repeating until 6th position

4 until 10 position

from above series it is concluded that

position can be calculated by simply adding no's

now 1+2=3 i.e 2 is repeating until 3rd position

position of 4 can be calculated similarly, 1+2+3+4=10.

now for 100th position

add no's from

1 to 13 which gives 91

which means 13 will repeat until 91 position

from above it is concluded 14 will appear at 100th position

Clearly the ending position of the nth row (EPn)is the sum of all natural numbers upto n =n.(n+1)/2

Means n is 4

4(4+1)/2

=10

So 4 is repeating until 10th position