Arithmetic Series  The sum of the terms of an arithmetic sequence.

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Presentation transcript:

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 35 th term.

Board Drill Find the sum of the first 1000 natural numbers.

If a n is given a=first term, d=common difference, L=last term S n = n(a 1 +a n ) 2 S n = n[2a 1 +(n-1)d] 2 If a n is not given

Examples  1. Find the sum of the first 10 natural numbers.  Solution: a 1 = 1, a n = 10, n = 10 Sn = n (a1 + an ) 2 S 10 = 10 ( ) 2 S 10 = 10 (11) ÷ 2 S 10 = 55

EXAMPLE 1 Find the sum of the first 30 terms in the series … a=3, d=6, n=30 Using the formula S n = n[2a+(n-1)d] 2 S n = 30[2x3+(30-1)6] 2 S n = 15[6+(29x6)] S n = 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,…….a Find the sum of the first 20 terms of an arithmetic sequence whose first term is 5 and common difference is 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 37 th term.