Examples 1/2/3 are all arithmetic progression, and the summation formula is as follows.

Sn = na 1+n(n- 1)d/2

Where a 1 is the first term, d is the tolerance and n is the sum term.

Example 1, A 1 = 1, D = 1, N = 100.

Example 2, a 1=2, d=2, n=50.

Example 3, a 1= 1, d=2, n=50.

I know what puzzles you the most is the sum of terms, right?

So you can get, it should be easy to know the general formula of the sequence.

For example, the example 1 is An=n, so the sum term n= 100.

Example 2 is An=2n, so the sum term n= 100/2=50.

Example 3 is An=2n- 1, so the sum term n=99+ 1/2=50.

The transformation can be calculated by summation formula.

Sn = [n+(n- 1)+...+ 1]/(2n)

=[n * n+n(n- 1)*(- 1)/2]/2n

= (n+ 1)/4

Speak more clearly.

For example, sum of Sn=2+3+ ...+100.

You can see the general formula An=n+ 1, so n= 100- 1=99.

I hope I can give you some help and enlightenment