
First observe the sequence and simplify .

What we observed?
If you observe the denominator and terms the below relation you get:-.
- If denominator be n then at n the term of that pair the value is 1.
Ex:-
For n=2
The 2nd term of the pair is 1
For n=3
The third term of the pair is 1
For n=4
the fourth term of the pair is 1.
And so on
Now
Let's build a sequence
1=1
2=2+1=3
3=3+2+1=3+3=6
4=4+6=10
5=5+10=15
6=6+15=21
7=7+21=28
8=8+28=36
9=9+36=45
10=10+45=55
11=11+55=66
12=12+66=78
________________________
m th term is 5/11
- Observe the sequence build above.
The sequence pair of 11 lies between 55 and 66 .
Now
as per n rule (noted first)
- This pair has 11 terms
- So 5/11 will be the 5th term of this pair
Now


Solution:-2:-
Now observe the built sequence .
Now
48th term will lie between the pair of 10
Now
- for n=10 the pair has 10terms .
If we subtract the ending of 9th pair from 48 we get


We came to know that 48th term is the 3rd term of 10th pair .
So it is
