What is the valuve of the sum of

1+3+5+7+9+11 ...+ 1997 +1999 ?

2 answers

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

The sum of the members of a finite arithmetic progression is called an arithmetic series.

The sum S of the first n values of a finite sequence is given by the formula:

Sn=(n/2)*[2*a1+(n-1)*d]

In this case:

n=1000

a1=1

d=2

Sn=(1000/2)*[2*1+(1000-1)*2]

Sn=500*[2+999*2]

Sn=500*[2+1998]

Sn=500*2000

Sn=1,000,000
In this case:

1 is first term

3 is second term

5 is third term

7 is fourth term

etc

1999 is thousandth term

because that in your progression

n=1000