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High School Mathematics - 2
3.4 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: Find the sum of the series 2+5+8+11+14+........+152
3456
4563
3927

Q 2: Find the sum of the first ten terms in the arithmetic sequence -4, 0, 4, 8, . . .
230
140
160

Q 3: Find the sum of the first k integers of 1 + 2 + 3 + 4 + 5 ..........k
k(k+1)/2
(K+2)/2
(k+1)/2

Q 4: Find the sum of the arithmetic sequence 3 + 7 + 11 + 15 + иии + 99
1275
2145
1345

Q 5: Find the sum of the first k integers of 1 + 2 + 3 + 4 + 5 ..........100
5050
3540
6066

Q 6: Find the sum the first 20 terms of the sequence: 1, 3, 5, 7, 9, ...
270
350
400

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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