Name: ___________________

Date:___________________

kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

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.

Name: ___________________

Date:___________________

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

Q 1: Find the sum of the series 2+5+8+11+14+........+152
4563
3927
3456

Q 2: 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 3: What is the sum of the first one hundred even numbers? (Hint: The first 100 even integers are 2, 4, 6, ..., 200)
15050
10100
5050

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

Q 5: Find the sum of the arithmetic sequence 3 + 7 + 11 + 15 + иии + 99
1275
1345
2145

Q 6: Find the sum of the first ten terms in the arithmetic sequence -4, 0, 4, 8, . . .
230
160
140

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


Subscription to kwizNET Learning System costs less than $1 per month & offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements


© 2003-2007 kwizNET Learning System LLC. All rights reserved. This material may not be reproduced, displayed, modified or distributed without the express prior written permission of the copyright holder. For permission, contact info@kwizNET.com
For unlimited printable worksheets & more, go to http://www.kwizNET.com.