Arithmetic Series

The sum of the terms of an arithmetic sequence.

Board Drill

Find the sum of the first 300 natural numbers.

Board Drill

Find the sum of the sequence 2, 8, 14, 20, …until 35th term.

Board Drill

Find the sum of the first 1000 natural numbers.

If an is given

a=first term, d=common difference, L=last term

Sn = n(a1+an) 2

Sn = n[2a1+(n-1)d] 2If an is not given

Examples 1. Find the sum of the first 10 natural numbers. Solution: a1 = 1 , an = 10, n = 10

Sn = n (a1 + an ) 2 S10 = 10 ( 1 + 10 )

2 S10 = 10 (11) ÷ 2

S10 = 55

EXAMPLE 1Find the sum of the first 30 terms in the series 3+9+15+…

a=3, d=6, n=30

Using the formulaSn = n[2a+(n-1)d] 2Sn = 30[2x3+(30-1)6] 2Sn = 15[6+(29x6)]

Sn = 15x180 = 2700

Try this! Find the sum of the first 30 natural

numbers. Find the sum of the first 50 natural

numbers. Find the sum of the first 12 terms of the

arithmetic sequence 47, 50, 53…. Find the sum of the first 25 terms of the

sequence 1, 6, 11,….

Seatwork

Answer the following.1.Find the sum of the first 80 natural numbers.2.Find the sum of all odd numbers between 1 and 47 inclusive.3.Find the sum of the first 28 terms of the sequence 2, 6, 10, 14,…

4. Find the sum of the arithmetic sequence 3, 11, 19, 27,…….a26

5. Find the sum of the first 20 terms of an arithmetic sequence whose first term is 5 and common difference is -3.

6. Find the sum of all even numbers from 2 to 28.

7. Find the sum of the of the first 55 natural numbers.

8. Find the sum of the first 500 natural numbers.

9. Find the sum of the first 24 terms in the sequence -5, -3, -1, 1,….

10. Find the sum of the sequence 6, 13, 20,….until the 37th term.