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High School Mathematics - 2
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.

Name: ___________________

Date:___________________

High School Mathematics - 2
Sum of Arithmetic Series - Using Formula