8/6/2019 Tutorial Questions - Sequence and Series
1/3
Mathematics Standard LevelSequences and Series Assignment
_____________________________________________________________________________________________
SEQUENCES AND SERIES
1. Write the sum of each series using sigma notation:
(a) 15...7531 +++++ (b) 3333 25...987 ++++
(c)2031...
10111
87
75 ++ (d)
2...
164
93
42
11
n
n+++++
2. Find the sum of the following series:
(a) ( )=
+4
1
1k
k (b)=
5
1
1
k k(c) ( )[ ]
=
+8
1
11i
i
3. Determine the common difference, the fifth term, the nth term
and the 100th term
of each of the arithmetic sequences.
(a) ,...11,8,5,2 (b) ,...32,22,2,2 sss +++
4. (a) The 10th term of an arithmetic sequence is2
55and the second term is
2
7. Find the first
term of the sequence.
(b) Which term of the arithmetic sequence 1,4,7, is 88?
(c) If 4,x,y,z, 10 are in an arithmetic sequence, find the
values ofx ,y andz
5. In each case, the partial sum of an arithmetic series is
given. Find the sum:
(a) 401...951 ++++ (b) ( )=
+10
0
25.03k
k (c) ( )=
20
0
21n
n
6. (a) Find the sum of the even numbers between 199 and 1999
(b) The sum of the first n terms of an arithmetic series is
)204(2
+nn .
(i) Write down the expression for the sum of the first )1( n
terms.
(ii) Find the first term and the common difference of the above
series.
7. Find the sum, to the number of terms given of the following
GPs:
(a) ...1263 +++ , 6 terms (b) 1+ ...,4
1
2
1++ 20 terms
8. (a) Find the common ratio, given that it is negative, of a GP
whose first term is 8 and
whose fifth term is21 .
(b) Find the sum of the first n terms of the GP ...16
25
4
51 +++ and find the least value ofn
for which the sum exceeds 20.(c) Find the sum of the first ten
terms of the geometric sequence ,...32,16,8,4
9. Find the sum of 9 + 27 + 81 ++ 729
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8/6/2019 Tutorial Questions - Sequence and Series
3/3
Mathematics Standard LevelSequences and Series Assignment
_____________________________________________________________________________________________
ANSWERS
1. (a) =
8
1
12r
r (b) =
+19
1
3)6(
r
r (c) =
+
++
14
1
1
6
32)1(
r
r
r
r(d)
=
n
r r
r
12
2. (a) 14 (b)60172 (c) 8
3. (a) 3 , 14 , 13 n , 299 (b) s , s42+ , sn )1(2 + , s992 +
4. (a)2
1(b) 30th (c)
2
18,7,
2
15
5. (a) 20301 (b) 46.75 (c) 399
6. (a) 989100 (b) (i) )4)(1(2 + nn ii) 12=a , 4=d
7. (a) 189 (b)19
2
12
8. (a)2
1, 2 (b)
= 14
54
n
nS , 9=n (c) 1364
9. 1089
10. (a) 3,-3 (b) 6,-6
11.32
3 , 32
12. (a)3
1(b)
495
106
13. (b)2
1>x (c)
16
11,3
2
14. (b)2
33)12( 1 + +rr
15. )1.1(20000RM ,2)1.1(20000RM , 15 years
16. 8 years
17. RM23.30
3
