Maths Quest C Year 11 for Queensland
WorkSHEET 9.2
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2
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Chapter 9 Sequences and series
Sequences and series
A sequence is defined by tn+1 = 3tn – 2, t1 = 0.2.
Generate the next 2 terms, t2 and t3.
Write down the first 3 terms of the arithmetic
sequence defined by
tn = 8  2n, n  {1, 2, 3, …}.
Explain why tn:{0.25, 0.20, 0.15, …} is an
arithmetic sequence.
WorkSHEET 9.2
1
Name: ___________________________
t 2  3  0.2  2  1.4
2
t 3  3   1.4  2  6.2
The next 2 terms are 1.4 and 6.2.
t1  8  2  1  6
3
t2  8  2  2  4
t3  8  2  3  1
The 3 terms are 6, 4, and 2.
t2  t1  0.20  0.25  0.05
2
t3  t2  0.15  0.20  0.05
 Common difference  0.05
Thus, it is an arithmetic sequence.
4
Find the sum to first 9 terms of the arithmetic
sequence tn:{11, 8, 5, …}.
a  11, d  3
2
9
S 9  [2   11  (9  1)  3]
2
S 9  4.5[22  24]
S 9  4 .5  2
S9  9
5
Explain why tn:{3, 1.2, 0.48, …} is a
geometric sequence.
t2  1.2

 0.4
t1
3
1
t3 0.48

 0.4
t2  1.2
 Common ratio  0.4
Thus, it is a geometric sequence.
6
Find the 12th term of a geometric sequence
with first term 0.3 and common ratio 2.
a  0.3, r  2
t12  0.3  (2)
t12  614.4
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Maths Quest C Year 11 for Queensland
7
Chapter 9 Sequences and series
The 4th term of a geometric sequence is 2 and
the 7th term is 54. Determine the first term of
this sequence.
WorkSHEET 9.2
ar 3  2
[1]
2
3
ar 6  54 [2]
Divide [2] by [1].
54
r3 
2
3
r  27
r  3 27
r3
Now replace r in [1].
a  33  2
a  27  2
2
a
27
8
The 3 consecutive terms of a geometric
sequence are 3.6, y, 22.5. Find the value of y.
y   3.6  22.5
2
y   81
y9
9
Find the sum of the first 10 terms of a
geometric sequence tn:{0.2, 0.6, 1.8, …}.
S10
S10
S10
S10
10
0 .6
3
0 .2
0.2(310 1)

3 1
0.2(59049  1)

2
0.2  59048

2
 5904.8
a  0.2, r 
 30, r  0.5
a

1 r
30

1  0.5
30

0.5
S   60 g
The total shampoo washed away is 60 g.
The amount of shampoo washed away from
a
Anita’s hair after successive washes was
S
recorded as 30 g in the first wash, 15 g in the
second wash, 7.5 g in the third wash and so on.
Determine the total amount of shampoo washed S 
away after infinite washes.
S
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