MAT 117
Arithmetic Sequences 4.4
Name_____________________
Find the 40th term of the following arithmetic sequences
a40  2  40  13
1.
2, 5, 8,11, ...
2.
25 , 26.5 , 28 , 29.5 ,...
3.
The 12th term of an arithmetic sequence is 32, and the 5th term is 18. Find the 20th term.
 119
a40  25  40  1 0.5
 44.5
32  a1  11d
18  a1  42 
a 20  10  192 
18  a1  4d
18  a1  8
a 20  48
14  7 d
a1  10
d 2
4.
The first term of an arithmetic sequence is 1, and the common difference is 4. Is 11,937 a term of this sequence? If so,
which one?
11937  1  n  1 4
11936  4n  4
11940  4n
n  2985
Yes, it’s the 2985th term
Find the sums of the following arithmetic sequences
5.
1  5  9  ...  405
405  1  n  1 4
S102 
102
1  405
2
 20706
404  4n  4
S102
408  4n
n  102
20
6.
21
 2n  1  2  1  39
k 0
 399
7.
An architect designs a theater with 15 seats in the first row, 18 in the second, 21 in the third, and so on. If the theater is to
have a seating capacity of 870, how many rows must the architect use in his design?
n
215  n  13
2
n
870  30  3n  3
2
1740  3n 2  27 n
870 
8.
An arithmetic sequence has first term
be added to get a sum of 702?
n 2  27 n  580  0
n  29n  20  0
n  20
a  78 and common difference d  4 .
n
278  n  1 4
2
1404  n 156  4n  4 
n 2  160n  351  0
1404  4n 2  160n
n  27 n  13  0
702 
4n 2  160n  1404  0
Yes, there are 2 answers. If you don’t believe it, write out the terms.
How many terms of this sequence must
n  13 or n  27