Name
9-4
Class
Date
Homework
Arithmetic Series
Find the sum of each finite arithmetic series.
1. 1 + 3 + 5 +
+ 99
Find the number of terms.
an  a1  (n  1)d
99  1  (n  1)2
99  1  2n  2
100  2n
50  n
2. 3 + 7 + 11 + 15 +
Find the sum.
n
Sn  (a1  an )
2
50
S50  (1  99)
2
+ 55
Find the number of terms. Find the sum.
n
an = a1 + (n − 1)d
Sn  (a1  an )
2
= 25(100)
=
3. 5 + 8 + 11 + … + 26
4. 4 + 9 + 14 + … + 44
5. 125 + 126 + 127 + …. + 131
Write each arithmetic series in summation notation.
6. 3 + 8 + 13 + … + 268
Find an explicit formula
for the nth term.
Find the value of n for 268.
268 = 5n − 2
an  a1  (n  1)d
270 = 5n
an  3  (n  1)5
54 = n
Write the summation notation.
an  5n  2
7. 4 + 8 + 12 + 16
8. 1 + 3 + 5 + … + 13
9. 3 + 7 + 11 + … + 31
10. 15 + 25 + 35 + … + 75
11.Given the series:
a)1+ 4+7+ ………..+63 what term is 63? Find the sum of the series.
b) 32+28+24+20+………. find the sum of 25 terms of the series.
12.Write a rule for the arithmetic sequence given a3  11 and a12  38
Find the sum of each finite series.
4
13.
 (n  1)
6
14.
n 1
n2
8
15.
 (n  25)
n 3
 (2n  1)
6
16.
 (3n  2)
n 3
Determine whether each list is a sequence or a series and finite or infinite.
17. 7, 12, 17, 22, 27
18. 3 + 5 + 7 + 9 + …
19. 8, 8.2, 8.4, 8.6, 8.8, 9.0, …
20. 1 + 5 + 9 + … + 21