Arithmetic series

What is an arithmetic series?

The sum of the terms of an arithmetic sequence

What does Sn mean

The sum of the n terms of a series

How do you prove that the sum of the first 100 natural numbers is 5050

S100= 1 + 2 + 3 + … + 98 + 99 + 100 (1)

S100=100 + 99 + 98 + … + 3 + 2 + 1 (2)

Adding (1) and ()

2 x S100 = 100 × 101

S100= (100 × 101)/ 2

=5050

What are natural numbers?

Positive integers

What is the Sn of arithmetic series?

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

OR

Sn= n/ 2 (a + l)

where l is the last term

Prove that the sum of the first n terms of an arithmetic series is n/ 2 (2a +(n-1)d)

Sn= a + (a+d) + (a+2d) + … + (a+(n-2)d) + (a+(n-1)d) (1)

Sn= (a+(n-1)d) + (a+(n-2)d) + … + (a+2d) + (a+d) + a (2)

Adding (1) and (2)