Chapter(^3)
289
P1^
17 (i) 2
(ii) 40
(iii) n 2 (3n^ + 1)
(iv) n 2 (9n^ + 1)
18 (i) a + 4 d = 205; a + 18 d = 373
(ii) 12 tickets; 157
(iii) 28 books
●?^ (Page^ 86)
For example, in column A enter 1 in
cell A1 and fill down a series of step
1; then in B1 enter
=3^(A1-1)
then fill down column B. Look for
the value 177 147 in column B and
read off the value of n in column A.
An alternative approach is to use the
IF function to find the correct value.
●?^ (Page^ 87)
3.7 × 1011 tonnes. Less than 1.8 × 109 ;
perhaps 10^8 for China.
●?^ (Page^ 90)
The series does not converge so it
does not have a sum to infinity.
Exercise 3B (Page 91)
1 (i) Yes: r = 2, u 7 = 320
(ii) No
(iii) Yes: r = −1, u 7 = 1
(iv) Yes: r = 1, u 7 = 5
(v) No
(vi) Yes: ru= 21 , 7 = 323
(vii) No
2 (i) 384
(ii) 765
3 (i) 4
(ii) 81 920
4 (i) 9
(ii) 10th term
5 (i) 9
(ii) 4088
6 (i) 6
(ii) 267 (to 3 s.f.)
7 (i) 2
(ii) 3
(iii) 3069
8 (i) 21
(ii) 8
9 (i) 101
(ii) 79
(iii) S∞= 117
10 (i) 0.9
(ii) 45th
(iii) 1000
(iv) 44
11 (i) 0.2
(ii) 1
12 (i) r = 0.8; a = 25
(ii) a = 6; r = 4
13 (i) (^163)
(ii) (a) x = −8 or 2
(b) r = – 21 or 2
(iii) (a) 256
(b) 17023
14 (i) r=^13
(ii) (^5413)
1
×()
n–
(iii) (^81) ()^1 – ()^13
n
(iv) 81
(v) 11 terms
15 (i) 20, 10, 5, 2.5, 1.25
(ii) 0, 10, 15, 17.5, 18.75
(iii) First series geometric,
common ratio^12. Second
sequence not geometric as
there is no common ratio.
16 (i) 68th swing is the first less
than 1°
(ii) 241° (to nearest degree)
17 (i) Height after nth impact =
10 ×()^23
n
(ii) 59.0m (to 3 s.f.)
19 (i) (^23)
(ii) 243
(iii) 270
20 (i) a = 117; (d = −21)
(ii) a = 128; (r = 34 )
21 (i) (^23)
(ii) 5150
22 (i) a + 4 d; a + 14 d
(iii) 2.5
Activity 3.1 (Page 98)
(i) n–1 2
(ii) n–2 3
●?^ (Page^ 101)
1.61051. This is 1 + 5 × (0.1) +
10 × (0.1)^2 + 10 × (0.1)^3 + 5 × (0.1)^4
- 1 × (0.1)^5 and 1, 5, 10, 10, 5, 1 are
the binominal coefficients for n = 5.
Exercise 3C (Page 103)
1 (i) x^4 + 4 x^3 + 6 x^2 + 4 x + 1
(ii) 1 + 7 x + 21 x^2 + 35 x^3 + 35 x^4 - 21 x^5 + 7 x^6 + x^7
(iii) x^5 + 10 x^4 + 40 x^3 + 80 x^2 +
80 x + 32
(iv) 64 x^6 + 192 x^5 + 240 x^4 +
160 x^3 + 60 x^2 + 12 x + 1
(v) 16 x^4 − 96 x^3 + 216 x^2 − 216 x - 81
(vi) 8 x^3 + 36 x^2 y + 54 xy^2 + 27 y^3
(vii) x^3 − 6 x + (^12) x − (^) x^83
(viii) x^4 + 8 x + (^24) x 2 + (^32) x 5 + (^16) x 8
(ix) 243 x^10 − 810 x^7 + 1080 x^4 −
720 x + (^240) x 2 − (^32) x 5