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### High School Mathematics - 23.4 Sum of Arithmetic Series - Using Formula

 Method 2: Using Formulas Sn = n/2(a1 + an) Sn = n/2[a + (n-1)d] Sn = sum of n terms n = number of terms a1 = first term an = nth term d = difference Example: Find the sum of the first 30 terms of series 5 + 9 + 13 + 17 + . . . Solution: Here n = 30 a1 = 5 d = a2 - a1 = 9 - 5 = 4 30th term = a30 = a1 + (n-1)d = 5 + (30-1).4 = 5 + 29.4 = 121 Therefore: S30 = n/2(first term + last term) = n/2(a1 + an)= 30(5 + 121)/2 = 1890 Example: An auditorium has 20 rows of seats. There are 20 seats in the first row., 21 seats in the second row, 22 seats in the third row, and so on. How many seats are there in all 20 rows? Solution: The number of seats in the 20 rows form an arithmetic sequence in which the common difference is d = 1 nth term = a20 = a1 + (n-1)d = 20 + 19(1) = 20 + 19 = 39 Sum of 20 terms is: Sn = n/2 (a1 + a20) = 20/2 (20 + 39) = 10 (59) = 590 Directions: Find the sum of the arithmetic series. Also write at least 5 examples of your own.
 Q 1: What is the sum of the first one hundred even numbers? (Hint: The first 100 even integers are 2, 4, 6, ..., 200) 50501010015050 Q 2: Find the sum of the first 100 terms of (-101) + (-99) + (-97) + ...........-200-150200 Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!

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