Maths Quest C Year 11 for Queensland
WorkSHEET 9.1
1
Chapter 9 Sequences and series
Sequences and series
Determine the first 3 terms of the sequence
tn = 2n6, n  {1, 2, 3, …}.
WorkSHEET 9.1
1
Name: ___________________________
t1  2  1  6  4
3
t 2  2  2  6  2
t3  2  3  6  0
The first 3 terms are 4, 2, and 0.
2
Show that the sequence
tn:{0.9, 0.7, 0.5, …} is an arithmetic
sequence.
t 2  t1  0.7  0.9  0.2
2
t3  t 2  0.5  0.7  0.2
Common difference = 0.2
Thus, it is an arithmetic sequence.
3
Find the rule for the arithmetic sequence
1 3 5
tn:{ , , , …}.
8 8 8
a
1
2 1
, d  
8
8 4
1
1
t n   (n  1) 
8
4
1 n 1
tn   
8 4 4
1 n
tn   
8 4
This is the required rule.
3
4
Find the 10th term of the arithmetic sequence
tn:{10, 6, 2, …}.
a  10, d  4
t10  10  (10  1)  4
3
t10  10  9  4
t10  26
The 10th term is 26.
5
The 3 consecutive terms of an arithmetic
sequence are 3.6, y, 8.2. Find the value of y.
(3.6  8.2)
2
y  5.9
y
2
Maths Quest C Year 11 for Queensland
Chapter 9 Sequences and series
WorkSHEET 9.1
2
6
Insert 3 evenly spaced numbers between
2 and 10.
a
 2  (5  1)d
 2  4d
4d
 2, t 5  10
 10
 10
 12
12
d 
4
d 3
Thus we have – 2, 1, 4, 7, 10 evenly spaced.
4
7
Find the 10th term of the arithmetic sequence
where the first term is 5 and the 4th term is 17.
 5, t 4  17
 17
 17
 12
12
d 
3
d 4
Now find t10 :
t10  5  (10  1)  4
t10  5  9  4
t10  41
4
8
Find the difference between the 4th term and
the 10th term of the arithmetic sequence
tn:{2, 1, 4, …}.
a
5  (4  1)d
5  3d
3d
a  2, d  3
t 4  2  (4  1)   3
t4  2  3   3
t 4  7
t10  2  (10  1)  3
t10  2  9  3
t10  25
Difference  7   25
 18
3
Maths Quest C Year 11 for Queensland
9
Chapter 9 Sequences and series
The 10th term in an arithmetic sequence is 8
and the 4th term is 4. Determine the first
term a.
WorkSHEET 9.1
a  (10  1)d  t10
3
4
a  9d  8 [1]
a  (4  1)d  4
a  3d  4 [2]
Subtract [2] from [1]
6d  12
12
6
d 2
Now replace d in [1]
a  9 2  8
d
a  18  8
a  8  18
a  10
10
Find the sum to first 8 terms of the arithmetic
sequence tn:{14, 12, 10, …}.
a  14, d  2
8
S 8  [2   14  (8  1)  2]
2
S 8  4[28  14]
S 8  4   14
S 8  56
2